Answer:
T2=871.34 K = 598.19 °C
Explanation:
As the relation Pv^k=cte is not clear, I will assume that k=3
Now, the first step is to find the specific molar volume in state 1, we use ideal gas law to find it:
[tex]P_{1} \nu _{1}=RT_{1}\\\\P_{1}=100 kPa\simeq 1atm\\\\\nu _{1}=\frac{RT_{1}}{P_{1}} \\\\\nu _{1}=24.44L/mol[/tex]
Now, to find the value of v2, we use the polytropic relation:
[tex]P_{1} \nu _{1} ^{3}=P_{2} \nu _{2} ^{3}\\\\\nu _{2} ^{3}=\frac{P_{1} \nu _{1} ^{3}}{P_{2}} \\\\\nu _{2}=\sqrt[3]{\frac{P_{1} \nu _{1} ^{3}}{P_{2}}} \\\\\nu_{2}=14.29L/mol[/tex]
With the value of v2, we can calculate the temperature in the second state with ideal gas law:
[tex]P_{2} \nu _{2}=RT_{2}\\\\T_{2}=\frac{P_{2} \nu _{2}}{R} \\\\T_{2}=871.34K[/tex]
