A gas is contained in a large cylinder. As you add 325,000 J of heat to gas ther

Question

A gas is contained in a large cylinder. As you add 325,000 J of heat to gas there's a force pushing in the piston, compressing the gas from 0.83 m^3 to 0.45 m^3 What is the Change in the gasses internal energy for this process (Assume a constant pressure 240,000 Pa is maintained) B) A 227 L (60 gallon) hot water heater is trying to heat 10.0 degree C tap water (it's winter) up to 51 degree C (124 degree F). If the electric heating element for this tank is a 9, 400 W heater then how long will it take to heat up this water? (give answer in minutes)

Explanation / Answer

Let the constant pressure be P = 2,40,000 Pa.

Initial volume be V1 = 0.83 m3

Final volume V2 = 0.45 m3

Then the work done dW = P × ( V2 - V1 )

= 2,40,000 × ( 0.45 - 0.83 )

= - 2,40,000 × 0.38

= - 91,200 J

Negative sign indicates that work is done on gas.

Here heat energy added dQ = 3,25,000 J

From first law of thermodynamics ,

Heat energy dQ = dU + dW

So change in internal energy dU = dQ - dW

Here dW is negative, then dU = dQ + dW

= 3,25,000 + 91,200

= 4,17,200 J

Here since heat energy is added, it is positive.So Internal energy of the gas has increased.

B) Let the specific heat of water be C = 1 cal/g

Now volume of water be V = 227 L = 227 kg

So mass of the water M = 2,27,000 g

We know that 1 L water has a weight 1 kg

Initial temperature of water be T1 = 10

Final temperature of water be T2 = 51

Change in temperature be T = 51 - 10 = 41

Now heat energy absorbed Q = M × C × T

= 2,27,000 × 1 × 41

= 93,07,000 J

Now power of the heater P = 9,400 W = 9400 J/s

So we know that power P = energy / time .

Then Time = energy / power

So time taken to heat 227 L water is T = Q /P

T = 93,07,000 / 9400

= 990.106 sec

Time taken in minutes T = 990.106 / 60 = 16.5 minutes.

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