Question

One mole of an ideal monoatomic gas is initially at 300K. Find the final temperature if 200J of heat are added as follows: (a) at constant volume (b) at constant pressure.

Answer 1

$\huge\underline{\underline{\bf \orange{Question-}}}$

One mole of an ideal monoatomic gas is initially at 300K. Find the final temperature if 200J of heat are added as follows:

(a) at constant volume

(b) at constant pressure.

$\huge\underline{\underline{\bf \orange{Solution-}}}$

At constant Volume ➝

⠀⠀⠀⠀⠀⠀❏$\large{\boxed{\bf \blue{Q=nC_v\triangle T}}}$

$\implies{\sf 200=1×\dfrac{3R}{2}×\triangle T }$

$\implies{\sf \triangle T = \dfrac{400}{3R}}$

$\implies{\sf \triangle T = \dfrac{400}{3×8.31} }$

$\implies{\sf \triangle T =16K}$

$\implies{\bf \red{\triangle T = T_f- 300}}$

$\implies{\sf T_f=300+16}$

$\implies{\bf \red{T_f=316\:K}}$

At Constant Pressure ➝

⠀⠀⠀⠀⠀⠀⠀⠀❏$\large{\boxed{\bf \blue{Q=nC_p\triangle T} }}$

$\implies{\sf 200=1×\dfrac{5R}{2}×\triangle T}$

$\implies{\sf \triangle T = \dfrac{400}{5R} }$

$\implies{\sf \triangle T = \dfrac{400}{5×8.31} }$

$\implies{\sf \triangle T = 9.6\:K}$

$\implies{\bf \red{\triangle T = T_f-300}}$

$\implies{\sf T_f=9.6+300}$

$\implies{\bf \red{T_f=309.6K} }$

$\huge\underline{\underline{\bf \orange{Answer-}}}$

At Constant Volume = 316 K

At Constant Pressure = 309.6 K

Answer 2

The final temperature at constant volume is Tf = 316 K and at constant pressure is Tf = 309.6 K

Explanation:

(a) Q = nCVΔT

200=(1)(3 / 2 R)(Tf − 300)

or 200 = 1.5 × 8.31(Tf − 300)

Solving we get

Tf = 316 K

(b) Q = n CpΔT

200 = (1)(52 R) (Tf − 300)

or 200 = 2.5 × 8.31(Tf − 300)

Solving we get

Tf = 309.6 K

Hence the final temperature at constant volume is Tf = 316 K and at constant pressure is Tf = 309.6 K