Question

A 150 W electric heater operates for 12.0 min to heat an ideal gas in a cylinder. During this time, the gas expands from 3.00 L to 11.0 L against a constant pressure of 1.03 atm. What is the change in internal energy (in kJ) of the gas?

Answer 1

The change in internal energy of the gas is -718 J.

Step-by-step explanation:

The change in internal energy of the gas can be calculated using the equation:

ΔU = Q - W

Where ΔU is the change in internal energy, Q is the heat transferred to the gas, and W is the work done by the gas. In this case, Q = 117 J and W can be calculated using the equation:

W = P(V_f - V_i)

Where P is the constant pressure, V_f is the final volume, and V_i is the initial volume.

Substituting the given values, we have:

W = (1.03 atm)(11.0 L - 3.00 L)

Calculating W gives:

W = 8.24 atm L

Now we can substitute the values of Q and W into the first equation to find ΔU:

ΔU = 117 J - 8.24 atm L

Converting atm L to joules using the conversion factor 1 atm L = 101.3 J, we have:

ΔU = 117 J - (8.24 atm L)(101.3 J/atm L)

Simplifying, we get:

ΔU = 117 J - 835 J

ΔU = -718 J

Therefore, the change in internal energy of the gas is -718 J.

Answer 2

Answer: The change in internal energy of the gas is 108.835 kJ

Step-by-step explanation:

To calculate the work done for reversible expansion process, we use the equation:

`W=P\Delta V=-P(V_2-V_1)`

where,

W = work done

P = pressure = 1.03 atm

`V_1` = initial volume = 3.00 L

`V_2` = final volume = 11.0 L

Putting values in above equation, we get:

`W=-(1.03)* (11.0-3.00)=8.24L.atm=834.9J=0.835kJ` (Conversion factor: 1 L. atm = 101.325 J)

Calculating the heat from power:

`Q=P* t`

where,

Q = heat required

P = power = 150 W

t = time = 12 min = 720 s (Conversion factor: 1 min = 60 s)

Putting values in above equation:

`Q=150* 720=108000J=108kJ`

The equation for first law of thermodynamics follows:

`Q=dU+W`

where,

Q = total amount of heat required = 108 kJ

dU = Change in internal energy = ?

W = work done = -0.835 kJ

Putting values in above equation, we get:

`108kJ=dU+(-0.835)\\\\dU=(108+0.835)=108.835kJ`

Hence, the change in internal energy of the gas is 108.835 kJ