Question

Is the energy required to heat air from 295 to \(305 \mathrm{K}\) the same as the energy required to heat it from 345 to \(355 \mathrm{K} ?\) Assume the pressure remains constant in both cases.

Short answer

Answer: Yes, the energy required to heat air from 295 K to 305 K is the same as the energy required to heat it from 345 K to 355 K.

Step-by-step solution

Identify the given information and constants

The initial and final temperatures for both cases are given, and the pressure remains constant. We also need the specific heat capacity of air at constant pressure, which is approximately 29.1 J/mol·K.

Calculate the temperature change for each case

ΔT1 = T2 - T1 = 305 K - 295 K = 10 K ΔT2 = T4 - T3 = 355 K - 345 K = 10 K

Write the heat energy equation for each case

We will use the heat energy equation Q = mcΔT for both cases: Q1 = m × c × ΔT1 Q2 = m × c × ΔT2

Calculate the energy required for each case

We will now calculate the energy required to heat the air in each case using the temperature changes from Step 2 and the specific heat capacity at constant pressure for air: Q1 = m × 29.1 J/mol·K × 10 K Q2 = m × 29.1 J/mol·K × 10 K

Compare the energy required for each case

Since the mass of air (m) and the specific heat capacity at constant pressure (c) are the same for both cases, and the temperature changes (ΔT1 and ΔT2) are also the same, the energy required to heat the air in both cases will be the same: Q1 = Q2 Therefore, the energy required to heat air from 295 K to 305 K is the same as the energy required to heat it from 345 K to 355 K.