Question

PROBLEM 5 (Problem 4-145 in 7th edition) Consider a well-insulated horizontal rigid cylinder that is divided into two compartments by a piston that is free to move but does not allow either gas to leak into the other side. Initially, one side of the piston contains 1 m3 of N2 gas at 500 kPa and 120oC while the other side contains 1 m3 of He gas at 500 kPa and 40oC. Assume the piston is made of 8 kg of copper initially at the average temperature of the two gases on both sides. Now thermal equilibrium is established in the cylinder as a result of heat transfer through the piston. Using constant specific heats at room temperature, determine the final equilibrium temperature in the cylinder. What would your answer be if the piston were not free to move

Answer 1

The answer is "
`\bold{83.8^(\circ) \ C}`".

Step-by-step explanation:

Formula for calculating the mass in He:

`\to m = (PV)/(RT)\\`

`= (500 * 1)/( 2.0769 * (40 + 273))\\\\ = (500 )/( 2.0769 * 313)\\\\ = (500 )/( 650.0697)\\\\= 0.76914 \ Kg`

Formula for calculating the mass in
`N_2`:

`\to m = (PV)/(RT)\\`

`= (500 * 1)/( 0.2968 * (120+ 273))\\\\ = (500 )/( 0.2968 * 393)\\\\ = (500 )/( 116.6424)\\\\= 4.2866\ Kg`

by using the temperature balancing the equation:

`T' = (mcT (He) + mcT ( N_2 ))/( mc (He) + mc ( N_2))`

`= (0.76914 * 3.1156 * 313 + 4.2866 * 0.743 *393)/( 0.76914 * 3.1156 + 4.2866 * 0.743) \\\\ = 357 \ \ K \approx 83.8^(\circ) \ C`