Question

For water at 30C and 1 atm: a= 3.04x10^-4 k^-1 , k =4.52x10^-5 atm ^-1 = 4.46 x10^-10 m^2/N, cpm= 75.3j/9molk), Vm =18.1cm^3/mol . Find Cv,m of water at 30C and 1 atm

Answer 1

Answer:

$C_{vm}$ of water at 30C and 1 atm is 256.834 J/mol·K.

Explanation:

To solve the question, we note the Maxwell relation such as

$C_{pm}-C_{vm}=\frac{9T\alpha ^2 V }{K}$

Where:

$C_{pm}$ = Specific heat of gas at constant pressure = 75.3 J/mol·K

$C_{vm}$ = Specific heat of gas at constant volume = Required

T = Temperature = 30 °C = 303.15 K

α = Linear expansion coefficient = 3.04 × 10⁻⁴ K⁻¹

K = Volume comprehensibility = 4.52 × 10⁻⁵ atm⁻¹

Therefore,

75.3 - $C_v$ = $\frac{9\times 303.15 \times (3.04 \times 10^{-1} 1.81 \times 10^{-5} }{4.52 \times 10^{-5} }$

$C_{vm}$  = $\frac{9\times 303.15 \times (3.04 \times 10^{-1} 1.81 \times 10^{-5} }{4.52 \times 10^{-5} }$ - 75.3 = 256.834 J/mol·K.