Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K . The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K , then the rise in temperature of the gas in B is.

Question

Two cylinders A and B fitted with pistons contain equal amounts of an ideal diatomic gas at 300 K . The piston of A is free to move, while that of B is held fixed. The same amount of heat is given to the gas in each cylinder. If the rise in temperature of the gas in A is 30 K , then the rise in temperature of the gas in B is. (A) 30 K (B) 18 K (C) 50 K (D) 42 K

Tardigrade Admin · Accepted Answer

A is free to move; therefore, heat will be supplied at constant pressure.

Δ Q_{A} = n C_{P_{A}} Δ T_{A} \dots

(i)

B

is held fixed, therefore, heat will be supplied at constant volume.

Δ Q_{B} = n C_{V}_{B} Δ T_{B} .....

(ii)
But

Δ Q_{A} = Δ Q_{B}

n C_{P_{A}} Δ T_{A} = n C_{V_{B}} Δ T_{B}

Δ T_{B} = (\frac{C _{P}}{C _{V}}) Δ T_{A}

= γ (Δ T_{A}) (γ = 1.4 (diatomic) (Δ T_{A} = 30 K)

= (1.4) (30 K)

Δ T_{B} = 42 K

$30 K$

$18 K$

$50 K$

$42 K$

30K

18K

50K

42K

$30 K$

$18 K$

$50 K$

$42 K$