Question

A vertical piston-cylinder device initially contains 0.1 m^3 of air at 400 K and 100 kPa. At this initial condition, the piston is resting on a stop. The piston-cylinder device is connected to a supply line with air at 400 K and a pressure of 500 kPa. The valve between the supply line and the piston-cylinder device is opened and is left open until the pressure in the piston-cylinder device reaches 500 kPa. The piston is observed to start moving when the pressure in the cylinder is 200 kPa and the piston continues to rise until it reaches a second stop. At the second stop, the piston-cylinder volume is 0.2 m^3 . The final temperature and pressure in the piston-cylinder device are 440 K and 500 kPa, respectively. Determine the heat transfer to or from the piston-cylinder device for the filling process Determine heat transfer (kJ) during the entire process.

Answer 1

Answer:

$Q=-38.15kJ$

Explanation:

From the question we are told that

Piston-cylinder initial Volume of air $v_1=0.1 m^3$

Piston-cylinder initial temperature $T_1=400k$

Piston-cylinder initial pressure $P_1= 100kpa$

Supply line temperature$T_s=400k$

Supply line pressure $P_s= 500kpa$

Valve  final pressure $P_v=500kpa$

Piston movement pressure $P_m=200kpa$

Piston-cylinder final Volume of air$v_2=0.2 m^3$

Piston-cylinder final temperature $T_2=440k$

Piston-cylinder final pressure $P_2= 500kpa$

Generally the  equation for conservation of mass is mathematically given by

$Q=m_2 \mu_2-m_1 \mu_1 +W-(m_2-m_1)h$

where

Initial moment

$m_1=\frac{p_1 V_1}{RT_1}$

$m_1=\frac{100*0.1}{0.287*400}$

$m_1=8.7*10^-^2kg$

Final moment

$m_2=\frac{p_2 V_2}{RT_2}$

$m_1=\frac{500*0.3}{0.287*440}$

$m_1=79*10^{-2}kg$

Work done by Piston movement pressure

$W=Pd$

$W=P(v_2-v_1)$

$W=200(0.2-0.1))$

$W=20000J$

Heat function

$h=cT_1$

$h=1.005(400)$

$h=402$

Therefore

$Q=(0.792*0.718(440)-0.0871*0.718(400)+20-(0.792-0.087)*402))$

$Q=-38.15kJ$

It is given mathematically that the system lost  or dissipated Heat of

$Q=-38.15kJ$