360367
One mole of a gas occupies \(22.4\,lit\) at \(N.T.P.\) Calculate the difference between two molar specific heats of the gas. \(J = 4200\;J{\rm{/}}k\,cal\).
1 \(1.979\,k\,cal{\rm{/}}k\,mol\,K\)
2 \(2.378\,k\,cal{\rm{/}}k\,mol\,K\)
3 \(4.569\,k\,cal/k\,mol\,K\)
4 \(3.028\,k\,cal{\rm{/}}k\,mol\,K\)
Explanation:
\(V = 22.4\,\,{\text{litre}} = 22.4 \times {10^{ - 3}}\;{m^3},\;\) \(J = 4200\;J/k{\mkern 1mu} cal\) by ideal gas equation for one mole of a gas,\(R = \frac{{PV}}{T} = \frac{{1.013 \times {{10}^5} \times 22.4 \times {{10}^{ - 3}}}}{{273}}\) \({C_p} - {C_v} = \frac{R}{J} = \frac{{1.013 \times {{10}^5} \times 22.4}}{{273 \times 4200}} = 1.979\) \(k\,cal{\rm{/}}k\,mol\,K\)
PHXI13:KINETIC THEORY
360368
The molar specific heat at constant pressure of an ideal gas is \(\dfrac{7}{2} R\). The ratio of specific heat at constant pressure to that at constant volume is
1 \(\dfrac{7}{5}\)
2 \(\dfrac{8}{7}\)
3 \(\dfrac{5}{7}\)
4 \(\dfrac{9}{7}\)
Explanation:
Use Mayer's equation \(\begin{aligned}& C_{P}-C_{V}=R \\& C_{V}=\dfrac{7}{2} R-R=\dfrac{5}{2} R \\& \gamma=\dfrac{C_{P}}{C_{V}}=\dfrac{\dfrac{7}{2} R}{\dfrac{5}{2} R} \Rightarrow \gamma=\dfrac{7}{5}\end{aligned}\)
PHXI13:KINETIC THEORY
360369
A container contain \(0.1\;mol\) of \(H_{2}\) and \(0.1\;mol\) of \({O_2}\). If the gases are in thermal equilibrium then
1 Only the average kinetic energy of the molecule of \({H_2}\) and \({O_2}\) is same.
2 Average speed of the molecule of \({H_2}\) and \({O_2}\) is same.
3 Only the specific heat at constant pressure of two gases is same.
4 The specific heat at constant pressure and the kinetic energy are same for both the gases.
Explanation:
The specific heat at constant pressure \(\left(C_{P}\right)\) is the amount of heat required to raise the temperature of one gram through \(1^{\circ} \mathrm{C}\) when the pressure of the gas is kept constant. Again, the mean kinetic energy per molecule (3/2) \(k T\) depends only upon temperature. Clearly both the specific heats at constant pressure and mean kinetic energy are depending on the temperature which is again same for the two gases.
PHXI13:KINETIC THEORY
360370
Two moles of an ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{5}{3}\) are mixed with 3 moles of another ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{4}{3}\). The value of \(\dfrac{C_{P}}{C_{V}}\) for the mixture is
360371
The ratio of molar specific heats of oxygen is
1 1.4
2 1.67
3 1.33
4 1.28
Explanation:
Ratio of molar specific heats, \({\gamma=\dfrac{C_{P}}{C_{V}}}\) \({\gamma=1+\dfrac{2}{f}}\) \({f=}\) number of degrees of freedom \({f=5}\) for \({O_{2}}\) So \({\gamma=1+\dfrac{2}{5}=1.4}\)
360367
One mole of a gas occupies \(22.4\,lit\) at \(N.T.P.\) Calculate the difference between two molar specific heats of the gas. \(J = 4200\;J{\rm{/}}k\,cal\).
1 \(1.979\,k\,cal{\rm{/}}k\,mol\,K\)
2 \(2.378\,k\,cal{\rm{/}}k\,mol\,K\)
3 \(4.569\,k\,cal/k\,mol\,K\)
4 \(3.028\,k\,cal{\rm{/}}k\,mol\,K\)
Explanation:
\(V = 22.4\,\,{\text{litre}} = 22.4 \times {10^{ - 3}}\;{m^3},\;\) \(J = 4200\;J/k{\mkern 1mu} cal\) by ideal gas equation for one mole of a gas,\(R = \frac{{PV}}{T} = \frac{{1.013 \times {{10}^5} \times 22.4 \times {{10}^{ - 3}}}}{{273}}\) \({C_p} - {C_v} = \frac{R}{J} = \frac{{1.013 \times {{10}^5} \times 22.4}}{{273 \times 4200}} = 1.979\) \(k\,cal{\rm{/}}k\,mol\,K\)
PHXI13:KINETIC THEORY
360368
The molar specific heat at constant pressure of an ideal gas is \(\dfrac{7}{2} R\). The ratio of specific heat at constant pressure to that at constant volume is
1 \(\dfrac{7}{5}\)
2 \(\dfrac{8}{7}\)
3 \(\dfrac{5}{7}\)
4 \(\dfrac{9}{7}\)
Explanation:
Use Mayer's equation \(\begin{aligned}& C_{P}-C_{V}=R \\& C_{V}=\dfrac{7}{2} R-R=\dfrac{5}{2} R \\& \gamma=\dfrac{C_{P}}{C_{V}}=\dfrac{\dfrac{7}{2} R}{\dfrac{5}{2} R} \Rightarrow \gamma=\dfrac{7}{5}\end{aligned}\)
PHXI13:KINETIC THEORY
360369
A container contain \(0.1\;mol\) of \(H_{2}\) and \(0.1\;mol\) of \({O_2}\). If the gases are in thermal equilibrium then
1 Only the average kinetic energy of the molecule of \({H_2}\) and \({O_2}\) is same.
2 Average speed of the molecule of \({H_2}\) and \({O_2}\) is same.
3 Only the specific heat at constant pressure of two gases is same.
4 The specific heat at constant pressure and the kinetic energy are same for both the gases.
Explanation:
The specific heat at constant pressure \(\left(C_{P}\right)\) is the amount of heat required to raise the temperature of one gram through \(1^{\circ} \mathrm{C}\) when the pressure of the gas is kept constant. Again, the mean kinetic energy per molecule (3/2) \(k T\) depends only upon temperature. Clearly both the specific heats at constant pressure and mean kinetic energy are depending on the temperature which is again same for the two gases.
PHXI13:KINETIC THEORY
360370
Two moles of an ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{5}{3}\) are mixed with 3 moles of another ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{4}{3}\). The value of \(\dfrac{C_{P}}{C_{V}}\) for the mixture is
360371
The ratio of molar specific heats of oxygen is
1 1.4
2 1.67
3 1.33
4 1.28
Explanation:
Ratio of molar specific heats, \({\gamma=\dfrac{C_{P}}{C_{V}}}\) \({\gamma=1+\dfrac{2}{f}}\) \({f=}\) number of degrees of freedom \({f=5}\) for \({O_{2}}\) So \({\gamma=1+\dfrac{2}{5}=1.4}\)
360367
One mole of a gas occupies \(22.4\,lit\) at \(N.T.P.\) Calculate the difference between two molar specific heats of the gas. \(J = 4200\;J{\rm{/}}k\,cal\).
1 \(1.979\,k\,cal{\rm{/}}k\,mol\,K\)
2 \(2.378\,k\,cal{\rm{/}}k\,mol\,K\)
3 \(4.569\,k\,cal/k\,mol\,K\)
4 \(3.028\,k\,cal{\rm{/}}k\,mol\,K\)
Explanation:
\(V = 22.4\,\,{\text{litre}} = 22.4 \times {10^{ - 3}}\;{m^3},\;\) \(J = 4200\;J/k{\mkern 1mu} cal\) by ideal gas equation for one mole of a gas,\(R = \frac{{PV}}{T} = \frac{{1.013 \times {{10}^5} \times 22.4 \times {{10}^{ - 3}}}}{{273}}\) \({C_p} - {C_v} = \frac{R}{J} = \frac{{1.013 \times {{10}^5} \times 22.4}}{{273 \times 4200}} = 1.979\) \(k\,cal{\rm{/}}k\,mol\,K\)
PHXI13:KINETIC THEORY
360368
The molar specific heat at constant pressure of an ideal gas is \(\dfrac{7}{2} R\). The ratio of specific heat at constant pressure to that at constant volume is
1 \(\dfrac{7}{5}\)
2 \(\dfrac{8}{7}\)
3 \(\dfrac{5}{7}\)
4 \(\dfrac{9}{7}\)
Explanation:
Use Mayer's equation \(\begin{aligned}& C_{P}-C_{V}=R \\& C_{V}=\dfrac{7}{2} R-R=\dfrac{5}{2} R \\& \gamma=\dfrac{C_{P}}{C_{V}}=\dfrac{\dfrac{7}{2} R}{\dfrac{5}{2} R} \Rightarrow \gamma=\dfrac{7}{5}\end{aligned}\)
PHXI13:KINETIC THEORY
360369
A container contain \(0.1\;mol\) of \(H_{2}\) and \(0.1\;mol\) of \({O_2}\). If the gases are in thermal equilibrium then
1 Only the average kinetic energy of the molecule of \({H_2}\) and \({O_2}\) is same.
2 Average speed of the molecule of \({H_2}\) and \({O_2}\) is same.
3 Only the specific heat at constant pressure of two gases is same.
4 The specific heat at constant pressure and the kinetic energy are same for both the gases.
Explanation:
The specific heat at constant pressure \(\left(C_{P}\right)\) is the amount of heat required to raise the temperature of one gram through \(1^{\circ} \mathrm{C}\) when the pressure of the gas is kept constant. Again, the mean kinetic energy per molecule (3/2) \(k T\) depends only upon temperature. Clearly both the specific heats at constant pressure and mean kinetic energy are depending on the temperature which is again same for the two gases.
PHXI13:KINETIC THEORY
360370
Two moles of an ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{5}{3}\) are mixed with 3 moles of another ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{4}{3}\). The value of \(\dfrac{C_{P}}{C_{V}}\) for the mixture is
360371
The ratio of molar specific heats of oxygen is
1 1.4
2 1.67
3 1.33
4 1.28
Explanation:
Ratio of molar specific heats, \({\gamma=\dfrac{C_{P}}{C_{V}}}\) \({\gamma=1+\dfrac{2}{f}}\) \({f=}\) number of degrees of freedom \({f=5}\) for \({O_{2}}\) So \({\gamma=1+\dfrac{2}{5}=1.4}\)
360367
One mole of a gas occupies \(22.4\,lit\) at \(N.T.P.\) Calculate the difference between two molar specific heats of the gas. \(J = 4200\;J{\rm{/}}k\,cal\).
1 \(1.979\,k\,cal{\rm{/}}k\,mol\,K\)
2 \(2.378\,k\,cal{\rm{/}}k\,mol\,K\)
3 \(4.569\,k\,cal/k\,mol\,K\)
4 \(3.028\,k\,cal{\rm{/}}k\,mol\,K\)
Explanation:
\(V = 22.4\,\,{\text{litre}} = 22.4 \times {10^{ - 3}}\;{m^3},\;\) \(J = 4200\;J/k{\mkern 1mu} cal\) by ideal gas equation for one mole of a gas,\(R = \frac{{PV}}{T} = \frac{{1.013 \times {{10}^5} \times 22.4 \times {{10}^{ - 3}}}}{{273}}\) \({C_p} - {C_v} = \frac{R}{J} = \frac{{1.013 \times {{10}^5} \times 22.4}}{{273 \times 4200}} = 1.979\) \(k\,cal{\rm{/}}k\,mol\,K\)
PHXI13:KINETIC THEORY
360368
The molar specific heat at constant pressure of an ideal gas is \(\dfrac{7}{2} R\). The ratio of specific heat at constant pressure to that at constant volume is
1 \(\dfrac{7}{5}\)
2 \(\dfrac{8}{7}\)
3 \(\dfrac{5}{7}\)
4 \(\dfrac{9}{7}\)
Explanation:
Use Mayer's equation \(\begin{aligned}& C_{P}-C_{V}=R \\& C_{V}=\dfrac{7}{2} R-R=\dfrac{5}{2} R \\& \gamma=\dfrac{C_{P}}{C_{V}}=\dfrac{\dfrac{7}{2} R}{\dfrac{5}{2} R} \Rightarrow \gamma=\dfrac{7}{5}\end{aligned}\)
PHXI13:KINETIC THEORY
360369
A container contain \(0.1\;mol\) of \(H_{2}\) and \(0.1\;mol\) of \({O_2}\). If the gases are in thermal equilibrium then
1 Only the average kinetic energy of the molecule of \({H_2}\) and \({O_2}\) is same.
2 Average speed of the molecule of \({H_2}\) and \({O_2}\) is same.
3 Only the specific heat at constant pressure of two gases is same.
4 The specific heat at constant pressure and the kinetic energy are same for both the gases.
Explanation:
The specific heat at constant pressure \(\left(C_{P}\right)\) is the amount of heat required to raise the temperature of one gram through \(1^{\circ} \mathrm{C}\) when the pressure of the gas is kept constant. Again, the mean kinetic energy per molecule (3/2) \(k T\) depends only upon temperature. Clearly both the specific heats at constant pressure and mean kinetic energy are depending on the temperature which is again same for the two gases.
PHXI13:KINETIC THEORY
360370
Two moles of an ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{5}{3}\) are mixed with 3 moles of another ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{4}{3}\). The value of \(\dfrac{C_{P}}{C_{V}}\) for the mixture is
360371
The ratio of molar specific heats of oxygen is
1 1.4
2 1.67
3 1.33
4 1.28
Explanation:
Ratio of molar specific heats, \({\gamma=\dfrac{C_{P}}{C_{V}}}\) \({\gamma=1+\dfrac{2}{f}}\) \({f=}\) number of degrees of freedom \({f=5}\) for \({O_{2}}\) So \({\gamma=1+\dfrac{2}{5}=1.4}\)
360367
One mole of a gas occupies \(22.4\,lit\) at \(N.T.P.\) Calculate the difference between two molar specific heats of the gas. \(J = 4200\;J{\rm{/}}k\,cal\).
1 \(1.979\,k\,cal{\rm{/}}k\,mol\,K\)
2 \(2.378\,k\,cal{\rm{/}}k\,mol\,K\)
3 \(4.569\,k\,cal/k\,mol\,K\)
4 \(3.028\,k\,cal{\rm{/}}k\,mol\,K\)
Explanation:
\(V = 22.4\,\,{\text{litre}} = 22.4 \times {10^{ - 3}}\;{m^3},\;\) \(J = 4200\;J/k{\mkern 1mu} cal\) by ideal gas equation for one mole of a gas,\(R = \frac{{PV}}{T} = \frac{{1.013 \times {{10}^5} \times 22.4 \times {{10}^{ - 3}}}}{{273}}\) \({C_p} - {C_v} = \frac{R}{J} = \frac{{1.013 \times {{10}^5} \times 22.4}}{{273 \times 4200}} = 1.979\) \(k\,cal{\rm{/}}k\,mol\,K\)
PHXI13:KINETIC THEORY
360368
The molar specific heat at constant pressure of an ideal gas is \(\dfrac{7}{2} R\). The ratio of specific heat at constant pressure to that at constant volume is
1 \(\dfrac{7}{5}\)
2 \(\dfrac{8}{7}\)
3 \(\dfrac{5}{7}\)
4 \(\dfrac{9}{7}\)
Explanation:
Use Mayer's equation \(\begin{aligned}& C_{P}-C_{V}=R \\& C_{V}=\dfrac{7}{2} R-R=\dfrac{5}{2} R \\& \gamma=\dfrac{C_{P}}{C_{V}}=\dfrac{\dfrac{7}{2} R}{\dfrac{5}{2} R} \Rightarrow \gamma=\dfrac{7}{5}\end{aligned}\)
PHXI13:KINETIC THEORY
360369
A container contain \(0.1\;mol\) of \(H_{2}\) and \(0.1\;mol\) of \({O_2}\). If the gases are in thermal equilibrium then
1 Only the average kinetic energy of the molecule of \({H_2}\) and \({O_2}\) is same.
2 Average speed of the molecule of \({H_2}\) and \({O_2}\) is same.
3 Only the specific heat at constant pressure of two gases is same.
4 The specific heat at constant pressure and the kinetic energy are same for both the gases.
Explanation:
The specific heat at constant pressure \(\left(C_{P}\right)\) is the amount of heat required to raise the temperature of one gram through \(1^{\circ} \mathrm{C}\) when the pressure of the gas is kept constant. Again, the mean kinetic energy per molecule (3/2) \(k T\) depends only upon temperature. Clearly both the specific heats at constant pressure and mean kinetic energy are depending on the temperature which is again same for the two gases.
PHXI13:KINETIC THEORY
360370
Two moles of an ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{5}{3}\) are mixed with 3 moles of another ideal gas with \(\dfrac{C_{P}}{C_{V}}=\dfrac{4}{3}\). The value of \(\dfrac{C_{P}}{C_{V}}\) for the mixture is
360371
The ratio of molar specific heats of oxygen is
1 1.4
2 1.67
3 1.33
4 1.28
Explanation:
Ratio of molar specific heats, \({\gamma=\dfrac{C_{P}}{C_{V}}}\) \({\gamma=1+\dfrac{2}{f}}\) \({f=}\) number of degrees of freedom \({f=5}\) for \({O_{2}}\) So \({\gamma=1+\dfrac{2}{5}=1.4}\)
