Question

Argon contained in a closed, rigid tank, initially at 33.7°C, 2.1 bar, and a volume of 4.2 m3, is heated to a final pressure of 7.2 bar. Assuming the ideal gas model with k = 1.65 for the argon, determine the heat transfer, in kJ.

Answer 1

Answer:

total heat required to raise pressure from 2.1 bar to 7.2 bar is 3295.336 kJ

Explanation:

given data

temperature t1 =  33.7°C = 306.7 K

pressure p1 = 2.1 bar

volume v1 = 4.2 m³

pressure p2 = 7.2 bar

ideal gas model k = 1.65

solution

we know heat transfer in constant volume is express as

Q = m × Cv × (t2-t1)   .............1

and here gas constant is 208.13 J/Kg.k

specific heat constant volume Cv = $\frac{R}{K-1}$  

put here value

Cv = $\frac{208.13}{1.65-1}$  

Cv = 320.2 J/Kg.k  

and

we get mass of argon gas m is

P1 × V1 = m × R × T1

m = $\frac{2.1\times 10^5 \times 4.2}{208.13\times 306.7}$  

m = 13.817 kg

and

t2 = $\frac{7.2\times 306.7}{2.1}$  

t2 = 1051.54  K

and

put equation 1 we get

Q = 13.81 × 320.2 × (1051.54-306.7)

Q = 3295.336 kJ

so total heat required to raise pressure from 2.1 bar to 7.2 bar is 3295.336 kJ