139343
Four mole of hydrogen, two mole of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?
1 $\frac{16}{7} \mathrm{R}$
2 $\frac{7}{16} \mathrm{R}$
3 $\mathrm{R}$
4 $\frac{23}{7} \mathrm{R}$
Explanation:
D Hydrogen is diatomic gas, so $\mathrm{C}_{\mathrm{V}_{1}}$ for Hydrogen $=\frac{5}{2} \mathrm{R}$ Number of Hydrogen moles $\left(n_{1}\right)=4$ For Helium (monoatomic) $\left(\mathrm{C}_{\mathrm{V}_{2}}\right)=\frac{3 \mathrm{R}}{2}$ No. of moles of $\mathrm{He}\left(\mathrm{n}_{2}\right)=2$ Water vapour is polyatomic $\left(\mathrm{C}_{\mathrm{V}_{3}}\right)=\frac{6}{2} \mathrm{R}$ No. of moles of water $\left(n_{3}\right)=1$ Let, molar specific heat of mixture at constant volume is $\mathrm{C}_{\mathrm{v}}$. then, $C_{v}=\frac{n_{1} C_{v_{1}}+n_{2} C_{v_{2}}+n_{3} C_{V_{3}}}{n_{1}+n_{2}+n_{3}}$ $=\frac{4 \times \frac{5}{2} R+2 \times \frac{3}{2} R+1 \times \frac{6}{2} R}{4+2+1}$ $C_{v}=\frac{16 R}{7}$ We know that, $\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$ So, $\mathrm{C}_{\mathrm{P}}-\frac{16 \mathrm{R}}{7}=\mathrm{R}$ $\mathrm{C}_{\mathrm{P}}=\mathrm{R}+\frac{16}{7} \mathrm{R}$ $\mathrm{C}_{\mathrm{P}}=\frac{23}{7} \mathrm{R}$
BITSAT-2006
Kinetic Theory of Gases
139344
Which of the following relation is correct?
C At constant volume, $\Delta \mathrm{U}=\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}$ At constant pressure, But, $\Delta \mathrm{H}=\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}$ $\mathrm{H}=\mathrm{U}+\mathrm{PV}$ For 1 mole of gas, $\mathrm{PV}=\mathrm{RT}$ $\therefore \mathrm{H}=\mathrm{U}+\mathrm{RT}$ $\therefore \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta(\mathrm{RT})$ $\Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{R} \Delta \mathrm{T}$ $\Delta \mathrm{H}-\Delta \mathrm{U}=\mathrm{R} \Delta \mathrm{T}$ Let, substitute values of $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ in equation (i) $\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}-\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{R} \Delta \mathrm{T}$ $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=\mathrm{R}$
CG PET- 2015
Kinetic Theory of Gases
139345
In a isothermal process, specific heat of gas is
1 zero
2 negative
3 infinity
4 None of these
Explanation:
C By using formula, $\Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T}$ Where, $\mathrm{s}=$ specific heat In isothermal process $\Delta T=0$ $\Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T}$ $\mathrm{s}=\frac{\Delta \mathrm{Q}}{\mathrm{m} \Delta \mathrm{T}}$ In equation (i) if $\Delta T=0$, then $s=\infty$
139343
Four mole of hydrogen, two mole of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?
1 $\frac{16}{7} \mathrm{R}$
2 $\frac{7}{16} \mathrm{R}$
3 $\mathrm{R}$
4 $\frac{23}{7} \mathrm{R}$
Explanation:
D Hydrogen is diatomic gas, so $\mathrm{C}_{\mathrm{V}_{1}}$ for Hydrogen $=\frac{5}{2} \mathrm{R}$ Number of Hydrogen moles $\left(n_{1}\right)=4$ For Helium (monoatomic) $\left(\mathrm{C}_{\mathrm{V}_{2}}\right)=\frac{3 \mathrm{R}}{2}$ No. of moles of $\mathrm{He}\left(\mathrm{n}_{2}\right)=2$ Water vapour is polyatomic $\left(\mathrm{C}_{\mathrm{V}_{3}}\right)=\frac{6}{2} \mathrm{R}$ No. of moles of water $\left(n_{3}\right)=1$ Let, molar specific heat of mixture at constant volume is $\mathrm{C}_{\mathrm{v}}$. then, $C_{v}=\frac{n_{1} C_{v_{1}}+n_{2} C_{v_{2}}+n_{3} C_{V_{3}}}{n_{1}+n_{2}+n_{3}}$ $=\frac{4 \times \frac{5}{2} R+2 \times \frac{3}{2} R+1 \times \frac{6}{2} R}{4+2+1}$ $C_{v}=\frac{16 R}{7}$ We know that, $\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$ So, $\mathrm{C}_{\mathrm{P}}-\frac{16 \mathrm{R}}{7}=\mathrm{R}$ $\mathrm{C}_{\mathrm{P}}=\mathrm{R}+\frac{16}{7} \mathrm{R}$ $\mathrm{C}_{\mathrm{P}}=\frac{23}{7} \mathrm{R}$
BITSAT-2006
Kinetic Theory of Gases
139344
Which of the following relation is correct?
C At constant volume, $\Delta \mathrm{U}=\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}$ At constant pressure, But, $\Delta \mathrm{H}=\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}$ $\mathrm{H}=\mathrm{U}+\mathrm{PV}$ For 1 mole of gas, $\mathrm{PV}=\mathrm{RT}$ $\therefore \mathrm{H}=\mathrm{U}+\mathrm{RT}$ $\therefore \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta(\mathrm{RT})$ $\Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{R} \Delta \mathrm{T}$ $\Delta \mathrm{H}-\Delta \mathrm{U}=\mathrm{R} \Delta \mathrm{T}$ Let, substitute values of $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ in equation (i) $\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}-\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{R} \Delta \mathrm{T}$ $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=\mathrm{R}$
CG PET- 2015
Kinetic Theory of Gases
139345
In a isothermal process, specific heat of gas is
1 zero
2 negative
3 infinity
4 None of these
Explanation:
C By using formula, $\Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T}$ Where, $\mathrm{s}=$ specific heat In isothermal process $\Delta T=0$ $\Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T}$ $\mathrm{s}=\frac{\Delta \mathrm{Q}}{\mathrm{m} \Delta \mathrm{T}}$ In equation (i) if $\Delta T=0$, then $s=\infty$
NEET Test Series from KOTA - 10 Papers In MS WORD
WhatsApp Here
Kinetic Theory of Gases
139343
Four mole of hydrogen, two mole of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?
1 $\frac{16}{7} \mathrm{R}$
2 $\frac{7}{16} \mathrm{R}$
3 $\mathrm{R}$
4 $\frac{23}{7} \mathrm{R}$
Explanation:
D Hydrogen is diatomic gas, so $\mathrm{C}_{\mathrm{V}_{1}}$ for Hydrogen $=\frac{5}{2} \mathrm{R}$ Number of Hydrogen moles $\left(n_{1}\right)=4$ For Helium (monoatomic) $\left(\mathrm{C}_{\mathrm{V}_{2}}\right)=\frac{3 \mathrm{R}}{2}$ No. of moles of $\mathrm{He}\left(\mathrm{n}_{2}\right)=2$ Water vapour is polyatomic $\left(\mathrm{C}_{\mathrm{V}_{3}}\right)=\frac{6}{2} \mathrm{R}$ No. of moles of water $\left(n_{3}\right)=1$ Let, molar specific heat of mixture at constant volume is $\mathrm{C}_{\mathrm{v}}$. then, $C_{v}=\frac{n_{1} C_{v_{1}}+n_{2} C_{v_{2}}+n_{3} C_{V_{3}}}{n_{1}+n_{2}+n_{3}}$ $=\frac{4 \times \frac{5}{2} R+2 \times \frac{3}{2} R+1 \times \frac{6}{2} R}{4+2+1}$ $C_{v}=\frac{16 R}{7}$ We know that, $\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$ So, $\mathrm{C}_{\mathrm{P}}-\frac{16 \mathrm{R}}{7}=\mathrm{R}$ $\mathrm{C}_{\mathrm{P}}=\mathrm{R}+\frac{16}{7} \mathrm{R}$ $\mathrm{C}_{\mathrm{P}}=\frac{23}{7} \mathrm{R}$
BITSAT-2006
Kinetic Theory of Gases
139344
Which of the following relation is correct?
C At constant volume, $\Delta \mathrm{U}=\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}$ At constant pressure, But, $\Delta \mathrm{H}=\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}$ $\mathrm{H}=\mathrm{U}+\mathrm{PV}$ For 1 mole of gas, $\mathrm{PV}=\mathrm{RT}$ $\therefore \mathrm{H}=\mathrm{U}+\mathrm{RT}$ $\therefore \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta(\mathrm{RT})$ $\Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{R} \Delta \mathrm{T}$ $\Delta \mathrm{H}-\Delta \mathrm{U}=\mathrm{R} \Delta \mathrm{T}$ Let, substitute values of $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ in equation (i) $\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}-\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{R} \Delta \mathrm{T}$ $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=\mathrm{R}$
CG PET- 2015
Kinetic Theory of Gases
139345
In a isothermal process, specific heat of gas is
1 zero
2 negative
3 infinity
4 None of these
Explanation:
C By using formula, $\Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T}$ Where, $\mathrm{s}=$ specific heat In isothermal process $\Delta T=0$ $\Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T}$ $\mathrm{s}=\frac{\Delta \mathrm{Q}}{\mathrm{m} \Delta \mathrm{T}}$ In equation (i) if $\Delta T=0$, then $s=\infty$
139343
Four mole of hydrogen, two mole of helium and one mole of water vapour form an ideal gas mixture. What is the molar specific heat at constant pressure of mixture?
1 $\frac{16}{7} \mathrm{R}$
2 $\frac{7}{16} \mathrm{R}$
3 $\mathrm{R}$
4 $\frac{23}{7} \mathrm{R}$
Explanation:
D Hydrogen is diatomic gas, so $\mathrm{C}_{\mathrm{V}_{1}}$ for Hydrogen $=\frac{5}{2} \mathrm{R}$ Number of Hydrogen moles $\left(n_{1}\right)=4$ For Helium (monoatomic) $\left(\mathrm{C}_{\mathrm{V}_{2}}\right)=\frac{3 \mathrm{R}}{2}$ No. of moles of $\mathrm{He}\left(\mathrm{n}_{2}\right)=2$ Water vapour is polyatomic $\left(\mathrm{C}_{\mathrm{V}_{3}}\right)=\frac{6}{2} \mathrm{R}$ No. of moles of water $\left(n_{3}\right)=1$ Let, molar specific heat of mixture at constant volume is $\mathrm{C}_{\mathrm{v}}$. then, $C_{v}=\frac{n_{1} C_{v_{1}}+n_{2} C_{v_{2}}+n_{3} C_{V_{3}}}{n_{1}+n_{2}+n_{3}}$ $=\frac{4 \times \frac{5}{2} R+2 \times \frac{3}{2} R+1 \times \frac{6}{2} R}{4+2+1}$ $C_{v}=\frac{16 R}{7}$ We know that, $\mathrm{C}_{\mathrm{P}}-\mathrm{C}_{\mathrm{V}}=\mathrm{R}$ So, $\mathrm{C}_{\mathrm{P}}-\frac{16 \mathrm{R}}{7}=\mathrm{R}$ $\mathrm{C}_{\mathrm{P}}=\mathrm{R}+\frac{16}{7} \mathrm{R}$ $\mathrm{C}_{\mathrm{P}}=\frac{23}{7} \mathrm{R}$
BITSAT-2006
Kinetic Theory of Gases
139344
Which of the following relation is correct?
C At constant volume, $\Delta \mathrm{U}=\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}$ At constant pressure, But, $\Delta \mathrm{H}=\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}$ $\mathrm{H}=\mathrm{U}+\mathrm{PV}$ For 1 mole of gas, $\mathrm{PV}=\mathrm{RT}$ $\therefore \mathrm{H}=\mathrm{U}+\mathrm{RT}$ $\therefore \Delta \mathrm{H}=\Delta \mathrm{U}+\Delta(\mathrm{RT})$ $\Delta \mathrm{H}=\Delta \mathrm{U}+\mathrm{R} \Delta \mathrm{T}$ $\Delta \mathrm{H}-\Delta \mathrm{U}=\mathrm{R} \Delta \mathrm{T}$ Let, substitute values of $\Delta \mathrm{H}$ and $\Delta \mathrm{U}$ in equation (i) $\mathrm{C}_{\mathrm{p}} \Delta \mathrm{T}-\mathrm{C}_{\mathrm{v}} \Delta \mathrm{T}=\mathrm{R} \Delta \mathrm{T}$ $\mathrm{C}_{\mathrm{p}}-\mathrm{C}_{\mathrm{v}}=\mathrm{R}$
CG PET- 2015
Kinetic Theory of Gases
139345
In a isothermal process, specific heat of gas is
1 zero
2 negative
3 infinity
4 None of these
Explanation:
C By using formula, $\Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T}$ Where, $\mathrm{s}=$ specific heat In isothermal process $\Delta T=0$ $\Delta \mathrm{Q}=\mathrm{ms} \Delta \mathrm{T}$ $\mathrm{s}=\frac{\Delta \mathrm{Q}}{\mathrm{m} \Delta \mathrm{T}}$ In equation (i) if $\Delta T=0$, then $s=\infty$