If R is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from 273 K to 373 K when no work is done is

Question

If R is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from 273 K to 373 K when no work is done is (A) 100 R (B) 150 R (C) 300 R (D) 500 R

Tardigrade Admin · Accepted Answer

As no work is done, therefore, ÎW = 0 According to first law of thermodynamics ÎQ = ÎU + ÎW = ÎU = nCVÎT=n((R/&gamma;-1))Δ T Here, n =2, &gamma;=(5/3) Δ T=T2-T1=(373-273)=100 K Δ Q=2×(R/((5)3-1))×100=300 R

Q. If $R$ is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from $273 K$ to $373 K$ when no work is done is

$100 R$

$150 R$

$300 R$

$500 R$

As no work is done, therefore, $Δ W = 0$ According to first law of thermodynamics
$Δ Q = Δ U + Δ W = Δ U = n C_{V} Δ T = n (\frac{R}{γ - 1}) Δ T$
Here, $n = 2, γ = \frac{5}{3}$
$Δ T = T_{2} - T_{1} = (373 - 273) = 100 K$
$Δ Q = 2 \times \frac{R}{( \frac{5}{3} - 1 )} \times 100 = 300 R$

Q. If R is universal gas constant, the amount of heat needed to raise the temperature of 2 moles of an ideal monoatomic gas from 273K to 373K when no work is done is

100R

150R

300R

500R