The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure P = aT-1 where a is a constant. Then, the work done by the gas is

Question

The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure P = aT-1 where a is a constant. Then, the work done by the gas is (A)  nRT  (B)  4 nRT  (C)  2 nRT  (D)  6 nRT

Tardigrade Admin · Accepted Answer

According to an ideal gas equation PV = nRT or V= (nRT/P) ∵ P = (a/T) (given) ...(i) ∴ V = (nRT2/a) ⇒ dV = (2nRT/a) dT ...(ii) Work done by the gas, dW = PdV or W = ∫ limitsT4T (a/T) (2nRT /a)dT (Using (i) and (ii) ) = [2n RT]T4T = 6nRT

Q. The temperature of $n$ moles of an ideal gas is increased from $T$ to $4 T$ through a process for which pressure $P = a T^{- 1}$ where a is a constant. Then, the work done by the gas is

$n RT$

$4 n RT$

$2 n RT$

$6 n RT$

Q. The temperature of n moles of an ideal gas is increased from T to 4T through a process for which pressure P=aT−1 where a is a constant. Then, the work done by the gas is

nRT

4nRT

2nRT

6nRT

According to an ideal gas equation PV=nRT or V=PnRT​ ∵P=Ta​ (given) ...(i) ∴V=anRT2​ ⇒dV=a2nRT​dT...(ii) Work done by the gas, dW=PdV or W=T∫4T​Ta​a2nRT​dT (Using (i) and (ii) ) =[2nRT]T4T​=6nRT

Q. The temperature of $n$ moles of an ideal gas is increased from $T$ to $4 T$ through a process for which pressure $P = a T^{- 1}$ where a is a constant. Then, the work done by the gas is

$n RT$

$4 n RT$

$2 n RT$

$6 n RT$