Equation of state of a perfect gas; work done compressing a gas — NEET & JEE Questions

Question 1 · difficulty L1 · recall

The equation of state for an ideal gas is

• A. $PV=nRT$
• B. $P=nR/T$
• C. $PV=RT/n$
• D. $PVT=nR$

Question 2 · difficulty L2 · understanding

For a fixed amount of ideal gas at constant temperature, if the volume is halved, the pressure becomes

• A. half
• B. unchanged
• C. double
• D. four times

Question 3 · difficulty L2 · understanding

For a fixed amount of ideal gas at constant pressure, volume is directly proportional to

• A. absolute temperature
• B. Celsius temperature only
• C. inverse absolute temperature
• D. molar mass only

Question 4 · difficulty L2 · understanding

When an ideal gas is compressed, the work done by an external agent on the gas is

• A. necessarily negative under the convention 'work on gas positive'
• B. positive under the convention 'work on gas positive'
• C. always zero
• D. independent of the process path

Question 5 · difficulty L3 · application

One mole of an ideal gas is at $300\,\text{K}$ and occupies $24.6\,\text{L}$. Approximately what is its pressure? Take $R=8.31\,\text{J mol}^{-1}\text{K}^{-1}$.

• A. 0.10 bar
• B. 0.50 bar
• C. 1.01 bar
• D. 10.1 bar

Question 6 · difficulty L3 · application

A fixed amount of ideal gas has pressure 2 bar and volume 3 L at constant temperature. If its volume becomes 6 L, what is the new pressure?

• A. 0.5 bar
• B. 1 bar
• C. 2 bar
• D. 4 bar

Question 7 · difficulty L3 · application

A gas expands at constant pressure $2.0\times10^5\,\text{Pa}$ from $0.010\,\text{m}^3$ to $0.016\,\text{m}^3$. What work is done by the gas?

• A. 600 J
• B. 1200 J
• C. 2000 J
• D. 3200 J

Question 8 · difficulty L3 · application

A gas is compressed at constant pressure $1.5\times10^5\,\text{Pa}$ from $8.0\times10^{-3}\,\text{m}^3$ to $5.0\times10^{-3}\,\text{m}^3$. What is the work done on the gas?

• A. $-450$ J
• B. 0 J
• C. 450 J
• D. 1200 J

Question 9 · difficulty L4 · application

A fixed amount of ideal gas changes from state $(P,V,T)$ to $(2P,V,2T)$. Is this change consistent with the ideal-gas equation?

• A. Yes
• B. No, pressure should be $4P$
• C. No, temperature should remain $T$
• D. No, volume should double

Question 10 · difficulty L4 · application

A gas is compressed quasistatically at constant pressure from volume $V$ to $V/2$. If the pressure is $P$, what is the work done on the gas?

• A. $PV/2$
• B. $PV$
• C. $2PV$
• D. $-PV/2$