Question

When 1.60×10⁵ J of heat transfer occurs into a meat pie initially at 20.0º C, its entropy increases by 480 J/K. What is its final temperature?

a) 30.0ºC
b) 35.0ºC
c) 40.0ºC
d) 45.0ºC

Answer 1

The final temperature of the meat pie, based on the entropy increase and heat transfer, is calculated to be approximately 353.33°C, which is not an option provided in the question. There might be a discrepancy in the question or options given.

Step-by-step explanation:

To find the final temperature of the meat pie, we can use the definition of entropy change given by the formula ΔS = Q/T, where ΔS is the change in entropy, Q is the heat transfer, and T is the absolute temperature in Kelvin.

Given that the entropy increases by 480 J/K when 1.60×10⁵ J of heat is transferred into the meat pie, we can rearrange the formula to solve for the final temperature:

ΔS = Q/T
⇒ T = Q/ΔS

Before we can calculate T, we need to convert the initial temperature from Celsius to Kelvin:

T_initial = 20.0°C = 20.0 + 273.15 = 293.15 K

Now we can find the final temperature by adding the heat transfer energy (in Kelvin) to the initial temperature:

T_final = T_initial + (Q/ΔS)
⇒ T_final = 293.15 K + (1.60×10⁵ J / 480 J/K)
⇒ T_final = 293.15 K + 333.33 K
⇒ T_final = 626.48 K

Converting back to Celsius:

T_final = 626.48 K - 273.15
⇒ T_final ≈ 353.33°C