Explain how the thermal energy of an isolated system changes with time if the mechanical energy of that system is constant.
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Answer:
The power decreases by 36%
Explanation:
Given:
At 20° C
Power, P₀ = 300 W
Potential difference, V = 150 volts
Now, power is given as
P = V²/R
where, R is the resistance
on substituting the values, we get
300 = 150²/R₀
or
R₀ = 75 Ω
Now, the variation of resistance with temperature is given as
R = R₀[1 + α(T - T₀)]
where, α is the temperature coefficient of resistivity = 0.0003125 (°C⁻¹)
now, at
T₀ = 20° C
R₀ = 75 Ω
for
T = 1820° C
we have
R = R₀[1 + α(T - T₀)]
substituting the values
we get
R = 75×[1 + 0.0003125 × (1820 - 20)]
or
R = 117.18 Ω
Now using the formula for power
We have,
P = V²/R
or
P = 150²/117.18 = 192 W
Therefore, the percentage change will be
=
on substituting the values , we get
=
= -36%
here, negative sign depicts the decrease in power