Question

An ideal monoatomic gas is confined in a cylinder by a spring-loaded piston if cross-section $8 \times 10^{- 3}m^{2}$. Initially the gas is at 300K and occupies a volume of $2.4 \times 10^{- 3}m^{3}$ and the spring is in a relaxed state. The gas is heated by a small heater coil H. The force constant of the spring is 8000 N/m, and the atmospheric pressure is $1.0 \times 10^{5}Pa$. The cylinder and piston are thermally insulated. The piston and the spring are massless and there is no friction between the piston and cylinder. There is no heat loss through heater coil wire leads and thermal capacity of the heater coil is negligible. With all the above assumptions, if the gas is heated by the heater until the piston moves out slowly by 0.1m, then the final temperature is

• A. (a) 400 K
• B. 800 K
• C. 1200 K
• D. 300 K

Answer 1

Answer: (D)

300 K

Answer 2

Number of moles in first vessel $\mu_{1} = \frac{P_{1}V}{RT_{1}}$ and number of

moles in second vessel $\mu_{2} = \frac{P_{2}V}{RT_{2}}$

If both vessels are joined together then quantity of gas

remains same i.e $\mu = \mu_{1} + \mu_{2}$

$\frac{P(2V)}{RT} = \frac{P_{1}V}{RT_{1}} + \frac{P_{2}V}{RT_{2}}$

$\frac{P}{T} = \frac{P_{1}}{2T_{1}} + \frac{P_{2}}{2T_{2}}$