07. Polytropic and Other Process
Thermodynamics

148508 During an experiment, an ideal gas is found to obey an additional law $V^{2}=$ constant. The gas is initially at temperature $T$ and volume. $V$. The temperature of the gas will be following, when it expands to a volume $2 \mathrm{~V}$ ?

1 $\sqrt{2} \mathrm{~T}$
2 $\sqrt{4} \mathrm{~T}$
3 $\sqrt{6} \mathrm{~T}$
4 $\sqrt{5} \mathrm{~T}$
Thermodynamics

148509 Two containers of equal volume contain the same gas at pressure $P_{1}$ and $P_{2}$ and absolute temperature $T_{1}$ and $T_{2}$ respectively. On joining the vessels the gas reaches a common pressure $P$ and common temperature $T$. The ratio $P / T$ is equal to

1 $\frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}}$
2 $\frac{P_{1} T_{1}+P_{2} T_{2}}{\left(T_{1}+T_{2}\right)^{2}}$
3 $\frac{P_{1} T_{2}+P_{2} T_{1}}{\left(T_{1}+T_{2}\right)^{2}}$
4 $\frac{\mathrm{P}_{1}}{2 \mathrm{~T}_{1}}+\frac{\mathrm{P}_{2}}{2 \mathrm{~T}_{2}}$
Thermodynamics

148510 2 moles of an ideal mono-atomic gas is carried from a state $\left(\mathrm{P}_{0}, \mathrm{~V}_{0}\right)$ to state $\left(2 \mathrm{P}_{0}, 2 \mathrm{~V}_{0}\right)$ along a straight line path in a $P-V$ diagram. The amount of heat absorbed by the gas in the process is given by

1 $3 \mathrm{P}_{0} \mathrm{~V}_{0}$
2 $\frac{9}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
3 $6 \mathrm{P}_{0} \mathrm{~V}_{0}$
4 $\frac{3}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
Thermodynamics

148512 If the coefficient of superficial expansion is $x$ times the coefficient of cubical expansion, then the value of $x$ is

1 2
2 $\frac{3}{2}$
3 $\frac{2}{3}$
4 $\frac{1}{2}$
Thermodynamics

148513 ' $m$ ' grams of a gas of molecular weight $M$ is flowing in an isolated tube velocity $v$. If the gas flow is suddenly stopped the rise in the temperature is : $(\gamma=$ ratio of specific heats, $\mathbf{R}=$ universal gas constant, $J=$ mechanical equivalent of heat).

1 $\frac{\operatorname{Mv}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
2 $\frac{\mathrm{m}}{\mathrm{M}} \frac{\mathrm{v}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
3 $\frac{m v^{2} \gamma}{2 \mathrm{RJ}}$
4 $\frac{\mathrm{Mv}^{2} \gamma}{2 \mathrm{RJ}}$
Thermodynamics

148508 During an experiment, an ideal gas is found to obey an additional law $V^{2}=$ constant. The gas is initially at temperature $T$ and volume. $V$. The temperature of the gas will be following, when it expands to a volume $2 \mathrm{~V}$ ?

1 $\sqrt{2} \mathrm{~T}$
2 $\sqrt{4} \mathrm{~T}$
3 $\sqrt{6} \mathrm{~T}$
4 $\sqrt{5} \mathrm{~T}$
Thermodynamics

148509 Two containers of equal volume contain the same gas at pressure $P_{1}$ and $P_{2}$ and absolute temperature $T_{1}$ and $T_{2}$ respectively. On joining the vessels the gas reaches a common pressure $P$ and common temperature $T$. The ratio $P / T$ is equal to

1 $\frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}}$
2 $\frac{P_{1} T_{1}+P_{2} T_{2}}{\left(T_{1}+T_{2}\right)^{2}}$
3 $\frac{P_{1} T_{2}+P_{2} T_{1}}{\left(T_{1}+T_{2}\right)^{2}}$
4 $\frac{\mathrm{P}_{1}}{2 \mathrm{~T}_{1}}+\frac{\mathrm{P}_{2}}{2 \mathrm{~T}_{2}}$
Thermodynamics

148510 2 moles of an ideal mono-atomic gas is carried from a state $\left(\mathrm{P}_{0}, \mathrm{~V}_{0}\right)$ to state $\left(2 \mathrm{P}_{0}, 2 \mathrm{~V}_{0}\right)$ along a straight line path in a $P-V$ diagram. The amount of heat absorbed by the gas in the process is given by

1 $3 \mathrm{P}_{0} \mathrm{~V}_{0}$
2 $\frac{9}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
3 $6 \mathrm{P}_{0} \mathrm{~V}_{0}$
4 $\frac{3}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
Thermodynamics

148512 If the coefficient of superficial expansion is $x$ times the coefficient of cubical expansion, then the value of $x$ is

1 2
2 $\frac{3}{2}$
3 $\frac{2}{3}$
4 $\frac{1}{2}$
Thermodynamics

148513 ' $m$ ' grams of a gas of molecular weight $M$ is flowing in an isolated tube velocity $v$. If the gas flow is suddenly stopped the rise in the temperature is : $(\gamma=$ ratio of specific heats, $\mathbf{R}=$ universal gas constant, $J=$ mechanical equivalent of heat).

1 $\frac{\operatorname{Mv}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
2 $\frac{\mathrm{m}}{\mathrm{M}} \frac{\mathrm{v}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
3 $\frac{m v^{2} \gamma}{2 \mathrm{RJ}}$
4 $\frac{\mathrm{Mv}^{2} \gamma}{2 \mathrm{RJ}}$
Thermodynamics

148508 During an experiment, an ideal gas is found to obey an additional law $V^{2}=$ constant. The gas is initially at temperature $T$ and volume. $V$. The temperature of the gas will be following, when it expands to a volume $2 \mathrm{~V}$ ?

1 $\sqrt{2} \mathrm{~T}$
2 $\sqrt{4} \mathrm{~T}$
3 $\sqrt{6} \mathrm{~T}$
4 $\sqrt{5} \mathrm{~T}$
Thermodynamics

148509 Two containers of equal volume contain the same gas at pressure $P_{1}$ and $P_{2}$ and absolute temperature $T_{1}$ and $T_{2}$ respectively. On joining the vessels the gas reaches a common pressure $P$ and common temperature $T$. The ratio $P / T$ is equal to

1 $\frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}}$
2 $\frac{P_{1} T_{1}+P_{2} T_{2}}{\left(T_{1}+T_{2}\right)^{2}}$
3 $\frac{P_{1} T_{2}+P_{2} T_{1}}{\left(T_{1}+T_{2}\right)^{2}}$
4 $\frac{\mathrm{P}_{1}}{2 \mathrm{~T}_{1}}+\frac{\mathrm{P}_{2}}{2 \mathrm{~T}_{2}}$
Thermodynamics

148510 2 moles of an ideal mono-atomic gas is carried from a state $\left(\mathrm{P}_{0}, \mathrm{~V}_{0}\right)$ to state $\left(2 \mathrm{P}_{0}, 2 \mathrm{~V}_{0}\right)$ along a straight line path in a $P-V$ diagram. The amount of heat absorbed by the gas in the process is given by

1 $3 \mathrm{P}_{0} \mathrm{~V}_{0}$
2 $\frac{9}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
3 $6 \mathrm{P}_{0} \mathrm{~V}_{0}$
4 $\frac{3}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
Thermodynamics

148512 If the coefficient of superficial expansion is $x$ times the coefficient of cubical expansion, then the value of $x$ is

1 2
2 $\frac{3}{2}$
3 $\frac{2}{3}$
4 $\frac{1}{2}$
Thermodynamics

148513 ' $m$ ' grams of a gas of molecular weight $M$ is flowing in an isolated tube velocity $v$. If the gas flow is suddenly stopped the rise in the temperature is : $(\gamma=$ ratio of specific heats, $\mathbf{R}=$ universal gas constant, $J=$ mechanical equivalent of heat).

1 $\frac{\operatorname{Mv}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
2 $\frac{\mathrm{m}}{\mathrm{M}} \frac{\mathrm{v}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
3 $\frac{m v^{2} \gamma}{2 \mathrm{RJ}}$
4 $\frac{\mathrm{Mv}^{2} \gamma}{2 \mathrm{RJ}}$
Thermodynamics

148508 During an experiment, an ideal gas is found to obey an additional law $V^{2}=$ constant. The gas is initially at temperature $T$ and volume. $V$. The temperature of the gas will be following, when it expands to a volume $2 \mathrm{~V}$ ?

1 $\sqrt{2} \mathrm{~T}$
2 $\sqrt{4} \mathrm{~T}$
3 $\sqrt{6} \mathrm{~T}$
4 $\sqrt{5} \mathrm{~T}$
Thermodynamics

148509 Two containers of equal volume contain the same gas at pressure $P_{1}$ and $P_{2}$ and absolute temperature $T_{1}$ and $T_{2}$ respectively. On joining the vessels the gas reaches a common pressure $P$ and common temperature $T$. The ratio $P / T$ is equal to

1 $\frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}}$
2 $\frac{P_{1} T_{1}+P_{2} T_{2}}{\left(T_{1}+T_{2}\right)^{2}}$
3 $\frac{P_{1} T_{2}+P_{2} T_{1}}{\left(T_{1}+T_{2}\right)^{2}}$
4 $\frac{\mathrm{P}_{1}}{2 \mathrm{~T}_{1}}+\frac{\mathrm{P}_{2}}{2 \mathrm{~T}_{2}}$
Thermodynamics

148510 2 moles of an ideal mono-atomic gas is carried from a state $\left(\mathrm{P}_{0}, \mathrm{~V}_{0}\right)$ to state $\left(2 \mathrm{P}_{0}, 2 \mathrm{~V}_{0}\right)$ along a straight line path in a $P-V$ diagram. The amount of heat absorbed by the gas in the process is given by

1 $3 \mathrm{P}_{0} \mathrm{~V}_{0}$
2 $\frac{9}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
3 $6 \mathrm{P}_{0} \mathrm{~V}_{0}$
4 $\frac{3}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
Thermodynamics

148512 If the coefficient of superficial expansion is $x$ times the coefficient of cubical expansion, then the value of $x$ is

1 2
2 $\frac{3}{2}$
3 $\frac{2}{3}$
4 $\frac{1}{2}$
Thermodynamics

148513 ' $m$ ' grams of a gas of molecular weight $M$ is flowing in an isolated tube velocity $v$. If the gas flow is suddenly stopped the rise in the temperature is : $(\gamma=$ ratio of specific heats, $\mathbf{R}=$ universal gas constant, $J=$ mechanical equivalent of heat).

1 $\frac{\operatorname{Mv}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
2 $\frac{\mathrm{m}}{\mathrm{M}} \frac{\mathrm{v}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
3 $\frac{m v^{2} \gamma}{2 \mathrm{RJ}}$
4 $\frac{\mathrm{Mv}^{2} \gamma}{2 \mathrm{RJ}}$
Thermodynamics

148508 During an experiment, an ideal gas is found to obey an additional law $V^{2}=$ constant. The gas is initially at temperature $T$ and volume. $V$. The temperature of the gas will be following, when it expands to a volume $2 \mathrm{~V}$ ?

1 $\sqrt{2} \mathrm{~T}$
2 $\sqrt{4} \mathrm{~T}$
3 $\sqrt{6} \mathrm{~T}$
4 $\sqrt{5} \mathrm{~T}$
Thermodynamics

148509 Two containers of equal volume contain the same gas at pressure $P_{1}$ and $P_{2}$ and absolute temperature $T_{1}$ and $T_{2}$ respectively. On joining the vessels the gas reaches a common pressure $P$ and common temperature $T$. The ratio $P / T$ is equal to

1 $\frac{P_{1}}{T_{1}}+\frac{P_{2}}{T_{2}}$
2 $\frac{P_{1} T_{1}+P_{2} T_{2}}{\left(T_{1}+T_{2}\right)^{2}}$
3 $\frac{P_{1} T_{2}+P_{2} T_{1}}{\left(T_{1}+T_{2}\right)^{2}}$
4 $\frac{\mathrm{P}_{1}}{2 \mathrm{~T}_{1}}+\frac{\mathrm{P}_{2}}{2 \mathrm{~T}_{2}}$
Thermodynamics

148510 2 moles of an ideal mono-atomic gas is carried from a state $\left(\mathrm{P}_{0}, \mathrm{~V}_{0}\right)$ to state $\left(2 \mathrm{P}_{0}, 2 \mathrm{~V}_{0}\right)$ along a straight line path in a $P-V$ diagram. The amount of heat absorbed by the gas in the process is given by

1 $3 \mathrm{P}_{0} \mathrm{~V}_{0}$
2 $\frac{9}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
3 $6 \mathrm{P}_{0} \mathrm{~V}_{0}$
4 $\frac{3}{2} \mathrm{P}_{0} \mathrm{~V}_{0}$
Thermodynamics

148512 If the coefficient of superficial expansion is $x$ times the coefficient of cubical expansion, then the value of $x$ is

1 2
2 $\frac{3}{2}$
3 $\frac{2}{3}$
4 $\frac{1}{2}$
Thermodynamics

148513 ' $m$ ' grams of a gas of molecular weight $M$ is flowing in an isolated tube velocity $v$. If the gas flow is suddenly stopped the rise in the temperature is : $(\gamma=$ ratio of specific heats, $\mathbf{R}=$ universal gas constant, $J=$ mechanical equivalent of heat).

1 $\frac{\operatorname{Mv}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
2 $\frac{\mathrm{m}}{\mathrm{M}} \frac{\mathrm{v}^{2}(\gamma-1)}{2 \mathrm{RJ}}$
3 $\frac{m v^{2} \gamma}{2 \mathrm{RJ}}$
4 $\frac{\mathrm{Mv}^{2} \gamma}{2 \mathrm{RJ}}$