i. What is the minimum heat extraction required by the laws of... · OlympiadBench #1400

Physics · thermodynamics

Problem

i. What is the minimum heat extraction

-d Q_{2, \text { min }}

required by the laws of thermodynamics to heat up the room by

d Q_{1}

? Given constants: ## Hot Pocket a. It's winter and you want to keep warm. The temperature is

T_{0}=263 \mathrm{~K}

outside and

T_{1}=290 \mathrm{~K}

in your room. You have started a fire, which acts as a hot reservoir at temperature

T_{2}=1800 \mathrm{~K}

. You want to add a small amount of heat

d Q_{1}

to your room. The simplest method would be to extract heat

-d Q_{2, \mathrm{dump}}=d Q_{1}

from the fire and directly transfer it to your room. However, it is possible to heat your room more efficiently. Suppose that you can exchange heat between any pair of reservoirs. You cannot use any external source of work, such as the electrical grid, but the work extracted from running heat engines can be stored and used without dissipation.

Related theory

thermodynamics

Browse the problem library