Q 51 :

When 300 J of heat is given to an ideal gas with $C_p=\frac{7}{2}R$ its temperature raises from $20°\text{C}$ to $50°\text{C}$ keeping its volume constant. The mass of the gas is (approximately) _______ g.    ($R=8.314\text{ \hspace{0.05em}J/mol.K}$)                   [2026]

Q 52 :

One mole of an ideal diatomic gas expands from volume V to 2V isothermally at a temperature 27$°C$ and does W joule of work. If the gas undergoes same magnitude of expansion adiabatically from 27$°C$ doing the same amount of work W, then its final temperature will be (close to) ______ $°C$.

$(\log ₑ2 = 0.693)$   [2026]

• −189

   

• −117

   

• −30

   

• −56

   

Q 53 :

The internal energy of a monoatomic gas is 3nRT. One mole of helium is kept in a cylinder having internal cross sectional area of 17 $cm²$ and fitted with a light movable frictionless piston. The gas is heated slowly by supplying 126 J heat. If the temperature rises by 4 $°C,$ then the piston will move ____ cm.
(atmospheric pressure = $10⁵$ Pa)   [2026]

• 15.5

   

• 1.45

   

• 14.5

   

• 1.55

   

Q 54 :

A diatomic gas $(\gamma =1.4)$ does 100 J of work when it is expanded isobarically. Then the heat given to the gas ______ J.      [2026]

Q 55 :

An insulated cylinder of volume $60 {\text{cm}}^3$ is filled with a gas at $27°\text{C}$ and 2 atmospheric pressure. Then the gas is compressed making the final volume as $20 {\text{cm}}^3$ while allowing the temperature to rise to $77°\text{C}$. The final pressure is __________ atmospheric pressure.      [2026]

Q 56 :

In the following p-V diagram, the equation of state along the curved path is given by ${(V-2)}^2=4ap,$ where a is a constant. The total work done in the closed path is   [2026]

• $-\frac{1}{a}$

   

• $+\frac{1}{3a}$

   

• $\frac{1}{2a}$

   

• $-\frac{1}{3a}$