One mole of an ideal mono atomic gas at temperature T0 expands slowly according to the law (P/V)= textconstant. If the final temperature is 2T0 , heat supplied to the gas isâ

Question

One mole of an ideal mono atomic gas at temperature T0 expands slowly according to the law (P/V)= textconstant. If the final temperature is 2T0 , heat supplied to the gas isâ (A) 2RT0 (B) RT0 (C) (3/2) textitRT0 (D) (1/2) textitRT0

Tardigrade Admin · Accepted Answer

In a process PVx = constant, molar heat capacity is given by C=(R/γ - 1)+(R/1 - x) As the process is (P/V)= textconstant. i.e PV-1 = constant, therefor, x = -1 For ideal monoatomic gas, γ = 5/3 ∴ C=(R/(5)3 - 1)+(R/1 - (-1))=(3 R/2)+(R/2)= text2 textitR Δ Q=nC(Δ T)=1(2 R)(2 T0 - T0)=2RT0

Q. One mole of an ideal mono atomic gas at temperature $T_{0}$ expands slowly according to the law $\frac{P}{V} = constant.$ If the final temperature is $2 T_{0}$ , heat supplied to the gas is

$2 R T_{0}$

$R T_{0}$

$\frac{3}{2} RT_{0}$

$\frac{1}{2} RT_{0}$

Q. One mole of an ideal mono atomic gas at temperature T0​ expands slowly according to the law VP​=constant. If the final temperature is 2T0​ , heat supplied to the gas is​

2RT0​

RT0​

23​RT0​

21​RT0​

In a process PVx = constant, molar heat capacity is given by C=γ−1R​+1−xR​ As the process is VP​=constant. i.e PV-1 = constant, therefor, x = -1 For ideal monoatomic gas, γ = 5/3 ∴C=35​−1R​+1−(−1)R​=23R​+2R​=2R ΔQ=nC(ΔT)=1(2R)(2T0​−T0​)=2RT0​

Q. One mole of an ideal mono atomic gas at temperature $T_{0}$ expands slowly according to the law $\frac{P}{V} = constant.$ If the final temperature is $2 T_{0}$ , heat supplied to the gas is

$2 R T_{0}$

$R T_{0}$

$\frac{3}{2} RT_{0}$

$\frac{1}{2} RT_{0}$