Having trouble with both of these questions If anyone could

Having trouble with both of these questions! If anyone could help that would be great. Thank you!

Neon gas in a piston-cylinder assembly undergoes p (bar) two processes, A and B, between the same two end states 1 and 2. The processes are shown and the states are given. Process A is defined by the relationship p = constant, Process B is defined by a constant-volume process to state 1\' followed by a constant-pressure process to state 2 A Process B two steps state 1\' followed by aProcess A Process A:_ pv = const. State 1: p1 1 bar, V1-1 m3, U1 400 kJ, State 2: p2-10 bar, V2 = 0.1 m3, U2-450 kJ, 1 V (m3) Using this information, and making reasonable assumptions about the piston- cylinder assembly, find a) the work W, in kJ, for each process A and B, b) the heat transfer Q, in kJ, for each process A and B

Solution

1. solution

Given at point 1

Pressure P₁ = 1bar = 100000 N/m²

Volume V₁ =1 m³

internal energy U₁ =400 kJ

Given at point 2

Pressure P₂ = 10bar =1000000 N/m²

Volume V₂ =0.1 m³

internal energy U₂ =450 kJ

Workdone by piston on gas to compress from point 1 to 2

By path A , As system is cylinder and piston we can assume that the work is closed system work

so Work done in isothermal process W_A= P₁V_{1 *}ln(P₁/P₂)

W_A= 100000*1*ln(1/10) =-230.26kJ \"-\" indicates work done on system

By path B , As system is cylinder and piston we can assume that the work is closed system work

in path B there are 2 steps 1- 1¹ is Isochoric process and work done in Ischoric process is 0 in Closed system

and 1¹ - 2 Work done in constant pressure process = P₂ (V₂ - V₁)

So Total work done in path B= 0 + P₂ (V₂ - V₁) = 1000000 *(0.1-1)

W_B= -900kJ \"-\" indicates work done on system

Heat Transfer from gas by compressing from point 1 to 2

By path A ,

so, Heat tranfer in isothermal process Q_A= P₁V_{1 *}ln(P₁/P₂)

Q_A= 100000*1*ln(1/10) =-230.26kJ \"-\" indicates Heat rejected from system

By path B ,

in path B there are 2 steps 1- 1¹ is Isochoric process Heat transfer Q_B1 = (U₁₁ - U₁)

and 1¹ - 2 Heat transfer in constant pressure process Q_B2= (U₂ - U₁₁) +P₂ (V₂ - V₁)

So Total Heat transfer in path B= (U₁₁ - U₁)  + (U₂ - U₁₁) +P₂ (V₂ - V₁) = (U₂ - U₁) + (1000000 *(0.1-1))

Q_B= ((450-400) -900)kJ =- 850kJ \"-\" indicates Heat rejected By system

2.

Heat Transfered from Component to air Q= 3W as the component is considered as the system so all the electric energy is converted to heat generated in it.

Component Surface temperature T_s can be calculated using Newton\'s law of cooling Q = h A (T_s - T_a)

h = heat transfer coeffcient = 100 Wm²/K

A= Surface Area of plate = 5* 10^-4 m²

T_s = Surface temperature in K

T_a = Air temperature in K = 25+273 = 298 K

Q = h A (T_s - T_a)

3 = 100 * 5* 10^-4 * (T_s - 298)

T_s = 298+60 =258K = 85⁰C

Surface temperature of component = 85⁰C