371448
Assertion : During rapid pumping of air in tyres air inside the tyre is hotter than atmospheric air. Reason : Adiabatic process occurs at very high rate.
1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
During rapid pumping of air into tires, the adiabatic process occurs at a high rate, leading to an increase in temperature. The air inside the tire becomes hotter than atmospheric air. So correct option is (1).
PHXI12:THERMODYNAMICS
371449
In an adiabatic process if pressure is increased by \(\dfrac{2}{3} \%\) if \(\dfrac{C_{P}}{C_{V}}=\dfrac{3}{2}\), then the volume decreases by about
371450
The volume of an ideal gas \({(\gamma=1.5)}\) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is
1 \({\dfrac{2}{\sqrt{5}}}\)
2 \({\dfrac{4}{5}}\)
3 \({\dfrac{16}{25}}\)
4 \({\dfrac{8}{5 \sqrt{5}}}\)
Explanation:
Given, \({\gamma=1.5, V_{1}=5}\) litre, \({V_{2}=4}\) litre For adiabatic process, \({P V^{\gamma}=}\) constant \({P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma} \Rightarrow P_{2}=P_{1}\left(\dfrac{V_{1}}{V_{2}}\right)^{\gamma}}\) \({\Rightarrow P_{2}=P_{1}\left(\dfrac{5}{4}\right)^{1.5}}\) \({\therefore \dfrac{P_{1}}{P_{2}}=\dfrac{4}{5} \times \sqrt{\dfrac{4}{5}}=\dfrac{8}{5 \sqrt{5}}}\) So, correct option is (4)
JEE - 2024
PHXI12:THERMODYNAMICS
371451
A thermally insulated vessel contains an ideal gas of molecular mass \(\mathrm{M}\) and ratio of specific heat \(\gamma\). It is moving with speed \(v\) and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
1 \(\dfrac{(\gamma-1)}{2 \gamma R} M v^{2}\)
2 \(\dfrac{\gamma M v^{2}}{2 R}\)
3 \(\dfrac{(\gamma-1)}{2 R} M v^{2}\)
4 \(\dfrac{(\gamma-1)}{2(\gamma+1) R} M v^{2}\)
Explanation:
As on heat is lost, therefore Loss of kinetic energy \(=\) Gain of internal energy of gas i.e., \(\dfrac{1}{2} m v^{2}=n C_{V} \Delta T \Rightarrow \dfrac{1}{2} m v^{2}=\dfrac{m}{M} \cdot \dfrac{R}{\gamma-1} \Delta T\) \(\Rightarrow \Delta T=\dfrac{M v^{2}(\gamma-1)}{2 R}\)
PHXI12:THERMODYNAMICS
371452
One mole of an ideal gas at an initial temperature of \(TK\) does \(6R\) joules of work adiabatically. If the ratio of specific heat of this gas at constant pressure and at constant volume is \(5 / 3\), the final temperature of gas will be
371448
Assertion : During rapid pumping of air in tyres air inside the tyre is hotter than atmospheric air. Reason : Adiabatic process occurs at very high rate.
1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
During rapid pumping of air into tires, the adiabatic process occurs at a high rate, leading to an increase in temperature. The air inside the tire becomes hotter than atmospheric air. So correct option is (1).
PHXI12:THERMODYNAMICS
371449
In an adiabatic process if pressure is increased by \(\dfrac{2}{3} \%\) if \(\dfrac{C_{P}}{C_{V}}=\dfrac{3}{2}\), then the volume decreases by about
371450
The volume of an ideal gas \({(\gamma=1.5)}\) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is
1 \({\dfrac{2}{\sqrt{5}}}\)
2 \({\dfrac{4}{5}}\)
3 \({\dfrac{16}{25}}\)
4 \({\dfrac{8}{5 \sqrt{5}}}\)
Explanation:
Given, \({\gamma=1.5, V_{1}=5}\) litre, \({V_{2}=4}\) litre For adiabatic process, \({P V^{\gamma}=}\) constant \({P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma} \Rightarrow P_{2}=P_{1}\left(\dfrac{V_{1}}{V_{2}}\right)^{\gamma}}\) \({\Rightarrow P_{2}=P_{1}\left(\dfrac{5}{4}\right)^{1.5}}\) \({\therefore \dfrac{P_{1}}{P_{2}}=\dfrac{4}{5} \times \sqrt{\dfrac{4}{5}}=\dfrac{8}{5 \sqrt{5}}}\) So, correct option is (4)
JEE - 2024
PHXI12:THERMODYNAMICS
371451
A thermally insulated vessel contains an ideal gas of molecular mass \(\mathrm{M}\) and ratio of specific heat \(\gamma\). It is moving with speed \(v\) and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
1 \(\dfrac{(\gamma-1)}{2 \gamma R} M v^{2}\)
2 \(\dfrac{\gamma M v^{2}}{2 R}\)
3 \(\dfrac{(\gamma-1)}{2 R} M v^{2}\)
4 \(\dfrac{(\gamma-1)}{2(\gamma+1) R} M v^{2}\)
Explanation:
As on heat is lost, therefore Loss of kinetic energy \(=\) Gain of internal energy of gas i.e., \(\dfrac{1}{2} m v^{2}=n C_{V} \Delta T \Rightarrow \dfrac{1}{2} m v^{2}=\dfrac{m}{M} \cdot \dfrac{R}{\gamma-1} \Delta T\) \(\Rightarrow \Delta T=\dfrac{M v^{2}(\gamma-1)}{2 R}\)
PHXI12:THERMODYNAMICS
371452
One mole of an ideal gas at an initial temperature of \(TK\) does \(6R\) joules of work adiabatically. If the ratio of specific heat of this gas at constant pressure and at constant volume is \(5 / 3\), the final temperature of gas will be
371448
Assertion : During rapid pumping of air in tyres air inside the tyre is hotter than atmospheric air. Reason : Adiabatic process occurs at very high rate.
1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
During rapid pumping of air into tires, the adiabatic process occurs at a high rate, leading to an increase in temperature. The air inside the tire becomes hotter than atmospheric air. So correct option is (1).
PHXI12:THERMODYNAMICS
371449
In an adiabatic process if pressure is increased by \(\dfrac{2}{3} \%\) if \(\dfrac{C_{P}}{C_{V}}=\dfrac{3}{2}\), then the volume decreases by about
371450
The volume of an ideal gas \({(\gamma=1.5)}\) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is
1 \({\dfrac{2}{\sqrt{5}}}\)
2 \({\dfrac{4}{5}}\)
3 \({\dfrac{16}{25}}\)
4 \({\dfrac{8}{5 \sqrt{5}}}\)
Explanation:
Given, \({\gamma=1.5, V_{1}=5}\) litre, \({V_{2}=4}\) litre For adiabatic process, \({P V^{\gamma}=}\) constant \({P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma} \Rightarrow P_{2}=P_{1}\left(\dfrac{V_{1}}{V_{2}}\right)^{\gamma}}\) \({\Rightarrow P_{2}=P_{1}\left(\dfrac{5}{4}\right)^{1.5}}\) \({\therefore \dfrac{P_{1}}{P_{2}}=\dfrac{4}{5} \times \sqrt{\dfrac{4}{5}}=\dfrac{8}{5 \sqrt{5}}}\) So, correct option is (4)
JEE - 2024
PHXI12:THERMODYNAMICS
371451
A thermally insulated vessel contains an ideal gas of molecular mass \(\mathrm{M}\) and ratio of specific heat \(\gamma\). It is moving with speed \(v\) and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
1 \(\dfrac{(\gamma-1)}{2 \gamma R} M v^{2}\)
2 \(\dfrac{\gamma M v^{2}}{2 R}\)
3 \(\dfrac{(\gamma-1)}{2 R} M v^{2}\)
4 \(\dfrac{(\gamma-1)}{2(\gamma+1) R} M v^{2}\)
Explanation:
As on heat is lost, therefore Loss of kinetic energy \(=\) Gain of internal energy of gas i.e., \(\dfrac{1}{2} m v^{2}=n C_{V} \Delta T \Rightarrow \dfrac{1}{2} m v^{2}=\dfrac{m}{M} \cdot \dfrac{R}{\gamma-1} \Delta T\) \(\Rightarrow \Delta T=\dfrac{M v^{2}(\gamma-1)}{2 R}\)
PHXI12:THERMODYNAMICS
371452
One mole of an ideal gas at an initial temperature of \(TK\) does \(6R\) joules of work adiabatically. If the ratio of specific heat of this gas at constant pressure and at constant volume is \(5 / 3\), the final temperature of gas will be
371448
Assertion : During rapid pumping of air in tyres air inside the tyre is hotter than atmospheric air. Reason : Adiabatic process occurs at very high rate.
1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
During rapid pumping of air into tires, the adiabatic process occurs at a high rate, leading to an increase in temperature. The air inside the tire becomes hotter than atmospheric air. So correct option is (1).
PHXI12:THERMODYNAMICS
371449
In an adiabatic process if pressure is increased by \(\dfrac{2}{3} \%\) if \(\dfrac{C_{P}}{C_{V}}=\dfrac{3}{2}\), then the volume decreases by about
371450
The volume of an ideal gas \({(\gamma=1.5)}\) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is
1 \({\dfrac{2}{\sqrt{5}}}\)
2 \({\dfrac{4}{5}}\)
3 \({\dfrac{16}{25}}\)
4 \({\dfrac{8}{5 \sqrt{5}}}\)
Explanation:
Given, \({\gamma=1.5, V_{1}=5}\) litre, \({V_{2}=4}\) litre For adiabatic process, \({P V^{\gamma}=}\) constant \({P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma} \Rightarrow P_{2}=P_{1}\left(\dfrac{V_{1}}{V_{2}}\right)^{\gamma}}\) \({\Rightarrow P_{2}=P_{1}\left(\dfrac{5}{4}\right)^{1.5}}\) \({\therefore \dfrac{P_{1}}{P_{2}}=\dfrac{4}{5} \times \sqrt{\dfrac{4}{5}}=\dfrac{8}{5 \sqrt{5}}}\) So, correct option is (4)
JEE - 2024
PHXI12:THERMODYNAMICS
371451
A thermally insulated vessel contains an ideal gas of molecular mass \(\mathrm{M}\) and ratio of specific heat \(\gamma\). It is moving with speed \(v\) and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
1 \(\dfrac{(\gamma-1)}{2 \gamma R} M v^{2}\)
2 \(\dfrac{\gamma M v^{2}}{2 R}\)
3 \(\dfrac{(\gamma-1)}{2 R} M v^{2}\)
4 \(\dfrac{(\gamma-1)}{2(\gamma+1) R} M v^{2}\)
Explanation:
As on heat is lost, therefore Loss of kinetic energy \(=\) Gain of internal energy of gas i.e., \(\dfrac{1}{2} m v^{2}=n C_{V} \Delta T \Rightarrow \dfrac{1}{2} m v^{2}=\dfrac{m}{M} \cdot \dfrac{R}{\gamma-1} \Delta T\) \(\Rightarrow \Delta T=\dfrac{M v^{2}(\gamma-1)}{2 R}\)
PHXI12:THERMODYNAMICS
371452
One mole of an ideal gas at an initial temperature of \(TK\) does \(6R\) joules of work adiabatically. If the ratio of specific heat of this gas at constant pressure and at constant volume is \(5 / 3\), the final temperature of gas will be
371448
Assertion : During rapid pumping of air in tyres air inside the tyre is hotter than atmospheric air. Reason : Adiabatic process occurs at very high rate.
1 Both Assertion and Reason are correct and Reason is the correct explanation of Assertion.
2 Both Assertion and Reason are correct but Reason is not the correct explanation of Assertion.
3 Assertion is correct but Reason is incorrect.
4 Assertion is incorrect but reason is correct.
Explanation:
During rapid pumping of air into tires, the adiabatic process occurs at a high rate, leading to an increase in temperature. The air inside the tire becomes hotter than atmospheric air. So correct option is (1).
PHXI12:THERMODYNAMICS
371449
In an adiabatic process if pressure is increased by \(\dfrac{2}{3} \%\) if \(\dfrac{C_{P}}{C_{V}}=\dfrac{3}{2}\), then the volume decreases by about
371450
The volume of an ideal gas \({(\gamma=1.5)}\) is changed adiabatically from 5 litres to 4 litres. The ratio of initial pressure to final pressure is
1 \({\dfrac{2}{\sqrt{5}}}\)
2 \({\dfrac{4}{5}}\)
3 \({\dfrac{16}{25}}\)
4 \({\dfrac{8}{5 \sqrt{5}}}\)
Explanation:
Given, \({\gamma=1.5, V_{1}=5}\) litre, \({V_{2}=4}\) litre For adiabatic process, \({P V^{\gamma}=}\) constant \({P_{1} V_{1}^{\gamma}=P_{2} V_{2}^{\gamma} \Rightarrow P_{2}=P_{1}\left(\dfrac{V_{1}}{V_{2}}\right)^{\gamma}}\) \({\Rightarrow P_{2}=P_{1}\left(\dfrac{5}{4}\right)^{1.5}}\) \({\therefore \dfrac{P_{1}}{P_{2}}=\dfrac{4}{5} \times \sqrt{\dfrac{4}{5}}=\dfrac{8}{5 \sqrt{5}}}\) So, correct option is (4)
JEE - 2024
PHXI12:THERMODYNAMICS
371451
A thermally insulated vessel contains an ideal gas of molecular mass \(\mathrm{M}\) and ratio of specific heat \(\gamma\). It is moving with speed \(v\) and it suddenly brought to rest. Assuming no heat is lost to the surroundings, its temperature increases by
1 \(\dfrac{(\gamma-1)}{2 \gamma R} M v^{2}\)
2 \(\dfrac{\gamma M v^{2}}{2 R}\)
3 \(\dfrac{(\gamma-1)}{2 R} M v^{2}\)
4 \(\dfrac{(\gamma-1)}{2(\gamma+1) R} M v^{2}\)
Explanation:
As on heat is lost, therefore Loss of kinetic energy \(=\) Gain of internal energy of gas i.e., \(\dfrac{1}{2} m v^{2}=n C_{V} \Delta T \Rightarrow \dfrac{1}{2} m v^{2}=\dfrac{m}{M} \cdot \dfrac{R}{\gamma-1} \Delta T\) \(\Rightarrow \Delta T=\dfrac{M v^{2}(\gamma-1)}{2 R}\)
PHXI12:THERMODYNAMICS
371452
One mole of an ideal gas at an initial temperature of \(TK\) does \(6R\) joules of work adiabatically. If the ratio of specific heat of this gas at constant pressure and at constant volume is \(5 / 3\), the final temperature of gas will be
