Question

A frictionless piston cylinder device is filled with benzene at a pressure of 3.94 MPa and a quality of 30%. The benzene is heated until the temperature reaches 345°C. Benzene data: Tc. = 564 K Pcr. = 4.92 MPa R = 0.1064 kJ/kg:K Cp = 0.502 +0.00252* T kJ/kg.K Using the generalized charts, determine the following: (a) The temperature in State 1, in K, (b) The work done during this process in kJ/kg, (c) The heat transferred to the benzene during this process in kJ/kg.

Answer 1

Step-by-step explanation:

Given that,

Pressure = 3.94 Mpa

Benzene data

`T_(c)=564 K`

`P_(cr)=4.92\ MPa`

`R=0.1064\ kJ/kg.K`

`C_(p)=0.502+0.00252\ T KJ/kg.K`

(a). We need to calculate the temperature

Using equation of ideal gas at constant volume

`(P_(1))/(T_(1))=(P_(2))/(T_(2))`

Put the value into the formula

`T_(1)=(P_(1)T_(2))/(P_(2))`

Put the value into the formula

`T_(1)=(564*3.94 )/(4.92)`

`T_(1)=451.6\ K`

(b). We need to calculate the work done

Here, the work done by the system is zero because this process is isochoric process in which the volume is constant.

(c). We need to calculate the heat transferred to the benzene during this process

Using formula of heat transferred

`\Delta Q=C_(v)dT`

`\Delta Q=(C_(p)-R)dT`

`\Delta Q=(C_(p)-R)*(T_(2)-T_(1))`

`\Delta Q=(0.502-0.1064)*((345+273)-451.6)`

`\Delta Q=65.82\ KJ/kg`

Hence, This is the required solution.