Two cylinders contain same amount of ideal monatomic gas. Same amount of heat is given to two cylinders. If temperature rise in cylinder A is T0 then temperature rise in cylinder B will be

Question

Two cylinders contain same amount of ideal monatomic gas. Same amount of heat is given to two cylinders. If temperature rise in cylinder A is T0 then temperature rise in cylinder B will be (A) (4/3) T0 (B) 2 T0 (C) (T0/2) (D) (5/3) T0

Tardigrade Admin · Accepted Answer

Cylinder A Free piston i.e., at constant pressure Cylinder B Fixed piston i.e., at constant volume Δ Q=Δ U n CP Δ T=n CV Δ T' CP T0=CV(Δ T)' Δ T'=(CP/CV) T0 =&gamma; T0=(5/3) T0

Q. Two cylinders contain same amount of ideal monatomic gas. Same amount of heat is given to two cylinders. If temperature rise in cylinder $A$ is $T_{0}$ then temperature rise in cylinder $B$ will be

$\frac{4}{3} T_{0}$

$2 T_{0}$

$\frac{T _{0}}{2}$

$\frac{5}{3} T_{0}$

Cylinder $A$
Free piston i.e., at
constant pressure
Cylinder $B$
Fixed piston i.e., at
constant volume
$Δ Q = Δ U$
$n C_{P} Δ T = n C_{V} Δ T^{'}$
$C_{P} T_{0} = C_{V} (Δ T)^{'}$
$Δ T^{'} = \frac{C _{P}}{C _{V}} T_{0}$
$= γ T_{0} = \frac{5}{3} T_{0}$

Q. Two cylinders contain same amount of ideal monatomic gas. Same amount of heat is given to two cylinders. If temperature rise in cylinder A is T0​ then temperature rise in cylinder B will be

34​T0​

2T0​

2T0​​

35​T0​