A thermally insulated 50ohm resistor carries a current of 1A for 1s. The initial temperature of the resistor is 10degree, its mass is 5g, and its specific heat capacity is 850j/kg/k. Calculate the change in entropy of the resistor and what is the change in entropy of the universe?
To calculate the change in entropy of the resistor, we can use the formula:
ΔS = mcΔT
where ΔS is the change in entropy, m is the mass of the resistor, c is the specific heat capacity, and ΔT is the change in temperature.
First, let's determine the change in temperature of the resistor. Since the resistor is thermally insulated, it does not exchange any heat with the surroundings. Therefore, all the energy supplied to the resistor will be converted into an increase in temperature.
The amount of energy supplied to the resistor can be calculated using the formula:
E = IVt
where E is the energy, I is the current, V is the voltage across the resistor, and t is the time.
Given that the current is 1A and the time is 1s, and using Ohm's law (V = IR), we can determine the voltage across the resistor.
V = IR = (1A)(50Ω) = 50V
Therefore, the energy supplied to the resistor is:
E = IVt = (1A)(50V)(1s) = 50J
Now, let's calculate the change in temperature of the resistor using the energy supplied:
E = mcΔT
ΔT = E / (mc) = 50J / (0.005kg)(850J/kg/K) = 11.76K
Since the initial temperature of the resistor is 10°C, we need to convert it to Kelvin:
T_initial = 10°C + 273.15 = 283.15K
Therefore, the final temperature of the resistor is:
T_final = T_initial + ΔT = 283.15K + 11.76K = 294.91K
Now we can calculate the change in entropy of the resistor:
ΔS = mcΔT = (0.005kg)(850J/kg/K)(11.76K) = 50.1J/K
To determine the change in entropy of the universe, we need to consider the surroundings. In this case, since the resistor is thermally insulated, it does not exchange any heat with the surroundings, and thus its entropy change is isolated from the rest of the universe. Therefore, the change in entropy of the universe would only be affected by external factors or processes not considered in this context.