An insulated rigid tank is divided into two equal parts by a partition. Initially, one part contains 4 kg of an ideal gas at 850 kPa and 40°C, and the other part is evacuated. The partition is now removed, and the gas expands into the entire tank. Determine the final temperature and pressure in the tank. (Round the final answers to the nearest whole number.)

Allowing ideal gas to expand in whole tank, therefore resisiting force in this process is zero. thus work done si also zero. considering ideal gas as system , there is no heat transefer during process of expansion.

Assuming : the gas act like ideal gas, change in kinetic and potential energy is negligible

from 1 st law we have

[tex]Q - W = \Delta U + \Delta E_p + \Delta E_k[/tex]

By taking consideration of above assumption we get

[tex]\Delta U = 0 [/tex]

i.e.[tex] U_1 =U_2[/tex]

from ideal gas equation we hvae

[tex]P_1 V_1 = m_1 RT_1[/tex]

[tex]P_2 V_2 = m_2 RT_2[/tex]

as internal energy remain same in both state therefore temperature remain same [tex]\frac{P_2 V_2}{P_1 V_1} = \frac{m_2 RT_2}{m_1 RT_1}[/tex]

[tex]P_2 V_2 = P_1 V_1[/tex]

as we knwo that [tex]V_2 = 2V_1[/tex]

therefore we have

[tex]P_2 =\frac{P_1}{2}[/tex]

= 425 kPa