Question

4.0 hours. If the room is heated electrically, find the cost due to the loss of heat through the window during that time. (The thermal conductivity of glass is 0.80 J/(s m degree C) and the cost per kilo-watt-hour for electricity is $0.10 .) The gas in a cylinder is initially at point A, where the pressure is p_A = 8.0 times 10^4 Pa and the volume is 20 L. The gas is taken through the following two processes: 1) isochoric heating from A to B (p_B = 1.2 times 10^4 Pa), 2) isobaric expansion from B to C (V_C = 30 L). Sketch the process on a pV diagram, and find a) the work done by the gas in each of the two processes. b) If the heat absorbed by the gas is 1200 J in the process AB and 3000 J in the process BC, find the change of its internal energy in these two processes. Estimate the intensity and sound level at the place 20 m away from a 25W speaker. (Neglect the loss of power in the air. The intensity of the reference level is I_0 = 1.0 times 10^-12 W/m^2.)

Answer 1

11.

The processes A to B and B to C are shown in figure below with solid line:

Pb Pa 20L 30L V

From A to B, the process is isochoric, i.e., the volume remains constant. So work done from A to B is zero.

For the process B to C, the pressure is P = 1.2X10⁵ Pa

So work done during B to C is,

W_BC = P(V₂ - V₁) = (1.2X10⁵ Pa)(30 L - 20 L) = (1.2X10⁵ Pa)10 L = (1.2X10⁵ Pa)X10X10^-3m³

or, W_BC = 1.2X10³ J

Total heat absorbed is ∆Q = 1200 J + 3000 J = 4200 J

Total work done is ∆W = W_BC = 1.2X10³ J

Let the change in internal energy during AB be ∆U_AB and during BC be  ∆U_BC

then we have,

∆Q_AB =   ∆W_AB + ∆U_AB

or, 1200 J = 0 +  ∆U_AB

So, ∆U_AB  = 1200 J

for BC we have,

∆Q_BC =   ∆W_BC+ ∆U_BC

or, 3000 J = 1200 J + ∆U_BC

or,  ∆U_BC = 1800 J

So net change in internal energy is ∆U = ∆U_AB + ∆U_BC = 1200J + 1800J = 3000 J

***************************************************************************************************

12.

At 25 m away intensity is

I = 25W/(4π(20m)²)

or, I = 5X10^-3W/m²

Sound level is,

β = 10log(I/I₀) = 10log[(5X10^-3W/m²)/(10^-12W/m²)]

or, β = 97 dB

***************************************************************************************************
This concludes the answers. Check the answer and let me know if it's correct. If you need any more clarification or correction, feel free to ask.....