A Gas equation for an adiabatic process $\mathrm{PV}^{\gamma}=$ constant Standard gas equation $\mathrm{PV}=\mathrm{RT} \text { (For one mole of gas) }$ $\mathrm{V}=\frac{\mathrm{RT}}{\mathrm{P}} \ldots . \text { (ii) }$ From equation (i) and (ii), $\mathrm{P}\left(\frac{\mathrm{T}}{\mathrm{P}}\right)^{\gamma} =\text { constant }$ $\mathrm{P} .\left(\frac{\mathrm{T}^{\gamma}}{\mathrm{P}^{\gamma}}\right) =\text { constant }$ $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma} =\text { constant }$ $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma} =\text { constant is true for adiabatic process. }$
EAMCET-2008
Thermodynamics
148505
A process in which there is no flow of heat between the system and surroundings is a/an
1 adiabatic process
2 cyclic process
3 isobaric process
4 isochoric process
5 isothermal process
Explanation:
A Adiabatic Process- A thermodynamic process where no flow of heat between the system and surrounding. Thermodynamics equations of heat $\mathrm{dQ}=\mathrm{dU}+\mathrm{dW}$ $\mathrm{dQ}=0 \text { (For adiabatic process) }$ $\mathrm{dU}=-\mathrm{dW}$ The system is thermally isolated from surroundings.
Kerala CEE 2021
Thermodynamics
148506
A given mass of gas at a pressure ' $P$ ' and absolute temperature ' $T$ ' obeys the law $P \propto T^{3}$ during an adiabatic process. The adiabatic bulk modulus of the gas at a pressure ' $P$ ' is
1 $\frac{2 P}{3}$
2 $\mathrm{P}$
3 $\frac{3 P}{2}$
4 $2 \mathrm{P}$
Explanation:
C Given that, $\mathrm{P} \propto \mathrm{T}^{3}$ $\mathrm{PV}=\mathrm{nRT}$ $\mathrm{T}=\frac{\mathrm{PV}}{\mathrm{nR}}$ $\mathrm{P} \propto\left(\frac{\mathrm{PV}}{\mathrm{nR}}\right)^{3}$ $\mathrm{P}^{2} \mathrm{~V}^{3}=$ constant Taking square root on both side of equation (i), $\mathrm{PV}^{3 / 2}=\mathrm{c}^{1 / 2}$ $\mathrm{PV}^{3 / 2}=\mathrm{c}$ Differentiating both side of equation (ii), $\mathrm{P} \frac{\mathrm{dV}^{3 / 2}}{\mathrm{dV}}+\mathrm{V}^{3 / 2} \frac{\mathrm{dP}}{\mathrm{dV}}=0$ $\frac{3}{2} \mathrm{PV}^{1 / 2}=-\mathrm{V}^{3 / 2} \frac{\mathrm{dP}}{\mathrm{dV}}$ $\frac{3}{2} \mathrm{P}=\frac{-\mathrm{dP}}{\mathrm{dV} / \mathrm{V}}$ Bulk modulus, $\mathrm{K}=\frac{-\mathrm{dP}}{(\mathrm{dV} / \mathrm{V})}$ $\therefore$ Bulk modulus, $\mathrm{K}=\frac{3}{2} \mathrm{P}$.
AP EAMCET-23.04.2019
Thermodynamics
148507
A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_{1}$ (in Kelvin) and the final temperature is $\alpha T_{i}$, the value of $\alpha$ is
A Gas equation for an adiabatic process $\mathrm{PV}^{\gamma}=$ constant Standard gas equation $\mathrm{PV}=\mathrm{RT} \text { (For one mole of gas) }$ $\mathrm{V}=\frac{\mathrm{RT}}{\mathrm{P}} \ldots . \text { (ii) }$ From equation (i) and (ii), $\mathrm{P}\left(\frac{\mathrm{T}}{\mathrm{P}}\right)^{\gamma} =\text { constant }$ $\mathrm{P} .\left(\frac{\mathrm{T}^{\gamma}}{\mathrm{P}^{\gamma}}\right) =\text { constant }$ $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma} =\text { constant }$ $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma} =\text { constant is true for adiabatic process. }$
EAMCET-2008
Thermodynamics
148505
A process in which there is no flow of heat between the system and surroundings is a/an
1 adiabatic process
2 cyclic process
3 isobaric process
4 isochoric process
5 isothermal process
Explanation:
A Adiabatic Process- A thermodynamic process where no flow of heat between the system and surrounding. Thermodynamics equations of heat $\mathrm{dQ}=\mathrm{dU}+\mathrm{dW}$ $\mathrm{dQ}=0 \text { (For adiabatic process) }$ $\mathrm{dU}=-\mathrm{dW}$ The system is thermally isolated from surroundings.
Kerala CEE 2021
Thermodynamics
148506
A given mass of gas at a pressure ' $P$ ' and absolute temperature ' $T$ ' obeys the law $P \propto T^{3}$ during an adiabatic process. The adiabatic bulk modulus of the gas at a pressure ' $P$ ' is
1 $\frac{2 P}{3}$
2 $\mathrm{P}$
3 $\frac{3 P}{2}$
4 $2 \mathrm{P}$
Explanation:
C Given that, $\mathrm{P} \propto \mathrm{T}^{3}$ $\mathrm{PV}=\mathrm{nRT}$ $\mathrm{T}=\frac{\mathrm{PV}}{\mathrm{nR}}$ $\mathrm{P} \propto\left(\frac{\mathrm{PV}}{\mathrm{nR}}\right)^{3}$ $\mathrm{P}^{2} \mathrm{~V}^{3}=$ constant Taking square root on both side of equation (i), $\mathrm{PV}^{3 / 2}=\mathrm{c}^{1 / 2}$ $\mathrm{PV}^{3 / 2}=\mathrm{c}$ Differentiating both side of equation (ii), $\mathrm{P} \frac{\mathrm{dV}^{3 / 2}}{\mathrm{dV}}+\mathrm{V}^{3 / 2} \frac{\mathrm{dP}}{\mathrm{dV}}=0$ $\frac{3}{2} \mathrm{PV}^{1 / 2}=-\mathrm{V}^{3 / 2} \frac{\mathrm{dP}}{\mathrm{dV}}$ $\frac{3}{2} \mathrm{P}=\frac{-\mathrm{dP}}{\mathrm{dV} / \mathrm{V}}$ Bulk modulus, $\mathrm{K}=\frac{-\mathrm{dP}}{(\mathrm{dV} / \mathrm{V})}$ $\therefore$ Bulk modulus, $\mathrm{K}=\frac{3}{2} \mathrm{P}$.
AP EAMCET-23.04.2019
Thermodynamics
148507
A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_{1}$ (in Kelvin) and the final temperature is $\alpha T_{i}$, the value of $\alpha$ is
A Gas equation for an adiabatic process $\mathrm{PV}^{\gamma}=$ constant Standard gas equation $\mathrm{PV}=\mathrm{RT} \text { (For one mole of gas) }$ $\mathrm{V}=\frac{\mathrm{RT}}{\mathrm{P}} \ldots . \text { (ii) }$ From equation (i) and (ii), $\mathrm{P}\left(\frac{\mathrm{T}}{\mathrm{P}}\right)^{\gamma} =\text { constant }$ $\mathrm{P} .\left(\frac{\mathrm{T}^{\gamma}}{\mathrm{P}^{\gamma}}\right) =\text { constant }$ $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma} =\text { constant }$ $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma} =\text { constant is true for adiabatic process. }$
EAMCET-2008
Thermodynamics
148505
A process in which there is no flow of heat between the system and surroundings is a/an
1 adiabatic process
2 cyclic process
3 isobaric process
4 isochoric process
5 isothermal process
Explanation:
A Adiabatic Process- A thermodynamic process where no flow of heat between the system and surrounding. Thermodynamics equations of heat $\mathrm{dQ}=\mathrm{dU}+\mathrm{dW}$ $\mathrm{dQ}=0 \text { (For adiabatic process) }$ $\mathrm{dU}=-\mathrm{dW}$ The system is thermally isolated from surroundings.
Kerala CEE 2021
Thermodynamics
148506
A given mass of gas at a pressure ' $P$ ' and absolute temperature ' $T$ ' obeys the law $P \propto T^{3}$ during an adiabatic process. The adiabatic bulk modulus of the gas at a pressure ' $P$ ' is
1 $\frac{2 P}{3}$
2 $\mathrm{P}$
3 $\frac{3 P}{2}$
4 $2 \mathrm{P}$
Explanation:
C Given that, $\mathrm{P} \propto \mathrm{T}^{3}$ $\mathrm{PV}=\mathrm{nRT}$ $\mathrm{T}=\frac{\mathrm{PV}}{\mathrm{nR}}$ $\mathrm{P} \propto\left(\frac{\mathrm{PV}}{\mathrm{nR}}\right)^{3}$ $\mathrm{P}^{2} \mathrm{~V}^{3}=$ constant Taking square root on both side of equation (i), $\mathrm{PV}^{3 / 2}=\mathrm{c}^{1 / 2}$ $\mathrm{PV}^{3 / 2}=\mathrm{c}$ Differentiating both side of equation (ii), $\mathrm{P} \frac{\mathrm{dV}^{3 / 2}}{\mathrm{dV}}+\mathrm{V}^{3 / 2} \frac{\mathrm{dP}}{\mathrm{dV}}=0$ $\frac{3}{2} \mathrm{PV}^{1 / 2}=-\mathrm{V}^{3 / 2} \frac{\mathrm{dP}}{\mathrm{dV}}$ $\frac{3}{2} \mathrm{P}=\frac{-\mathrm{dP}}{\mathrm{dV} / \mathrm{V}}$ Bulk modulus, $\mathrm{K}=\frac{-\mathrm{dP}}{(\mathrm{dV} / \mathrm{V})}$ $\therefore$ Bulk modulus, $\mathrm{K}=\frac{3}{2} \mathrm{P}$.
AP EAMCET-23.04.2019
Thermodynamics
148507
A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_{1}$ (in Kelvin) and the final temperature is $\alpha T_{i}$, the value of $\alpha$ is
A Gas equation for an adiabatic process $\mathrm{PV}^{\gamma}=$ constant Standard gas equation $\mathrm{PV}=\mathrm{RT} \text { (For one mole of gas) }$ $\mathrm{V}=\frac{\mathrm{RT}}{\mathrm{P}} \ldots . \text { (ii) }$ From equation (i) and (ii), $\mathrm{P}\left(\frac{\mathrm{T}}{\mathrm{P}}\right)^{\gamma} =\text { constant }$ $\mathrm{P} .\left(\frac{\mathrm{T}^{\gamma}}{\mathrm{P}^{\gamma}}\right) =\text { constant }$ $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma} =\text { constant }$ $\mathrm{P}^{1-\gamma} \mathrm{T}^{\gamma} =\text { constant is true for adiabatic process. }$
EAMCET-2008
Thermodynamics
148505
A process in which there is no flow of heat between the system and surroundings is a/an
1 adiabatic process
2 cyclic process
3 isobaric process
4 isochoric process
5 isothermal process
Explanation:
A Adiabatic Process- A thermodynamic process where no flow of heat between the system and surrounding. Thermodynamics equations of heat $\mathrm{dQ}=\mathrm{dU}+\mathrm{dW}$ $\mathrm{dQ}=0 \text { (For adiabatic process) }$ $\mathrm{dU}=-\mathrm{dW}$ The system is thermally isolated from surroundings.
Kerala CEE 2021
Thermodynamics
148506
A given mass of gas at a pressure ' $P$ ' and absolute temperature ' $T$ ' obeys the law $P \propto T^{3}$ during an adiabatic process. The adiabatic bulk modulus of the gas at a pressure ' $P$ ' is
1 $\frac{2 P}{3}$
2 $\mathrm{P}$
3 $\frac{3 P}{2}$
4 $2 \mathrm{P}$
Explanation:
C Given that, $\mathrm{P} \propto \mathrm{T}^{3}$ $\mathrm{PV}=\mathrm{nRT}$ $\mathrm{T}=\frac{\mathrm{PV}}{\mathrm{nR}}$ $\mathrm{P} \propto\left(\frac{\mathrm{PV}}{\mathrm{nR}}\right)^{3}$ $\mathrm{P}^{2} \mathrm{~V}^{3}=$ constant Taking square root on both side of equation (i), $\mathrm{PV}^{3 / 2}=\mathrm{c}^{1 / 2}$ $\mathrm{PV}^{3 / 2}=\mathrm{c}$ Differentiating both side of equation (ii), $\mathrm{P} \frac{\mathrm{dV}^{3 / 2}}{\mathrm{dV}}+\mathrm{V}^{3 / 2} \frac{\mathrm{dP}}{\mathrm{dV}}=0$ $\frac{3}{2} \mathrm{PV}^{1 / 2}=-\mathrm{V}^{3 / 2} \frac{\mathrm{dP}}{\mathrm{dV}}$ $\frac{3}{2} \mathrm{P}=\frac{-\mathrm{dP}}{\mathrm{dV} / \mathrm{V}}$ Bulk modulus, $\mathrm{K}=\frac{-\mathrm{dP}}{(\mathrm{dV} / \mathrm{V})}$ $\therefore$ Bulk modulus, $\mathrm{K}=\frac{3}{2} \mathrm{P}$.
AP EAMCET-23.04.2019
Thermodynamics
148507
A diatomic ideal gas is compressed adiabatically to $\frac{1}{32}$ of its initial volume. If the initial temperature of the gas is $T_{1}$ (in Kelvin) and the final temperature is $\alpha T_{i}$, the value of $\alpha$ is
