Answer:
the highest rate of heat transfer allowed is 0.9306 kW
Explanation:
Given the data in the question;
Volume = 4L = 0.004 m³
V[tex]_f[/tex] = V[tex]_g[/tex] = 0.002 m³
Using Table ( saturated water - pressure table);
at pressure p = 175 kPa;
v[tex]_f[/tex] = 0.001057 m³/kg
v[tex]_g[/tex] = 1.0037 m³/kg
u[tex]_f[/tex] = 486.82 kJ/kg
u[tex]_g[/tex] 2524.5 kJ/kg
h[tex]_g[/tex] = 2700.2 kJ/kg
So the initial mass of the water;
m₁ = V[tex]_f[/tex]/v[tex]_f[/tex] + V[tex]_g[/tex]/v[tex]_g[/tex]
we substitute
m₁ = 0.002/0.001057 + 0.002/1.0037
m₁ = 1.89414 kg
Now, the final mass will be;
m₂ = V/v[tex]_g[/tex]
m₂ = 0.004 / 1.0037
m₂ = 0.003985 kg
Now, mass leaving the pressure cooker is;
m[tex]_{out[/tex] = m₁ - m₂
m[tex]_{out[/tex] = 1.89414 - 0.003985
m[tex]_{out[/tex] = 1.890155 kg
so, Initial internal energy will be;
U₁ = m[tex]_f[/tex]u[tex]_f[/tex] + m[tex]_g[/tex]u[tex]_g[/tex]
U₁ = (V[tex]_f[/tex]/v[tex]_f[/tex])u[tex]_f[/tex] + (V[tex]_g[/tex]/v[tex]_g[/tex])u[tex]_g[/tex]
we substitute
U₁ = (0.002/0.001057)(486.82) + (0.002/1.0037)(2524.5)
U₁ = 921.135288 + 5.030387
U₁ = 926.165675 kJ
Now, using Energy balance;
E[tex]_{in[/tex] - E[tex]_{out[/tex] = ΔE[tex]_{sys[/tex]
QΔt - m[tex]_{out[/tex]h[tex]_{out[/tex] = m₂u₂ - U₁
QΔt - m[tex]_{out[/tex]h[tex]_g[/tex] = m₂u[tex]_g[/tex] - U₁
given that time = 75 min = 75 × 60s = 4500 sec
so we substitute
Q(4500) - ( 1.890155 × 2700.2 ) = ( 0.003985 × 2524.5 ) - 926.165675
Q(4500) - 5103.7965 = 10.06013 - 926.165675
Q(4500) = 10.06013 - 926.165675 + 5103.7965
Q(4500) = 4187.690955
Q = 4187.690955 / 4500
Q = 0.9306 kW
Therefore, the highest rate of heat transfer allowed is 0.9306 kW
