Practice Thermal Equilibrium in Physics

Use these practice problems to test your method after reviewing the concept explanation and worked examples.

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Quick Recap

Thermal equilibrium is the state in which objects in thermal contact have reached the same temperature, so there is no net transfer of thermal energy between them.

When two objects stop getting warmer or cooler because they have matched temperatures, they are in thermal equilibrium.

Showing a random 20 of 50 problems.

Example 1

hard
11 kg of ice at 0∘0^\circC is added to 22 kg of water at 80∘80^\circC. Assume the ice melts completely. (Lf=334000L_f = 334000 J/kg, cw=4200c_w = 4200 J/kg·∘^\circC.) Find the equilibrium temperature.

Example 2

challenge
An insulated tank holds 55 kg of water at 60∘60^\circC. Hot water at 80∘80^\circC is added until the tank temperature is 70∘70^\circC. Find the mass of hot water added.

Example 3

easy
Two objects are in thermal contact. Thermal equilibrium is reached when what is true of their temperatures?

Example 4

challenge
0.10.1 kg of steam at 100∘100^\circC is bubbled through 11 kg of water at 20∘20^\circC until all the steam condenses and equilibrium is reached. (Lv=2.26×106L_v = 2.26\times 10^6, cw=4200c_w = 4200.) Find the final temperature.

Example 5

hard
0.50.5 kg of steam at 100∘100^\circC is condensed into 22 kg of water at 20∘20^\circC. (Lv=2.26×106L_v = 2.26\times 10^6 J/kg, cw=4200c_w = 4200 J/kg·∘^\circC.) Find the equilibrium temperature.

Example 6

medium
11 kg of water at 20∘20^\circC is in a 0.30.3 kg aluminium pan (c=900c = 900) at 20∘20^\circC. A burner adds 2000020000 J. Find the final temperature.

Example 7

easy
Object A is at 50∘C50^\circ\text{C}, object B at 30∘C30^\circ\text{C}. Which way does heat flow when they touch?

Example 8

easy
200200 g of water at 80∘80^\circC is poured into 200200 g of water at 20∘20^\circC. Find the equilibrium temperature.

Example 9

medium
A 0.3 kg0.3 \text{ kg} aluminium spoon (c=900c=900) at 20∘C20^\circ\text{C} is placed in 0.5 kg0.5 \text{ kg} of soup (c=4000c=4000) at 80∘C80^\circ\text{C}. Find the equilibrium temperature.

Example 10

hard
A 0.20.2 kg block of aluminium (c=900c = 900) at TT is placed in 0.60.6 kg water at 25∘25^\circC (c=4200c = 4200). Equilibrium is 30∘30^\circC. Find TT.

Example 11

medium
Equal masses of two liquids (cA=2000c_A = 2000, cB=4000c_B = 4000) at 80∘80^\circC and 20∘20^\circC respectively are mixed. Find the equilibrium temperature.

Example 12

easy
11 kg of water at 40∘40^\circC is mixed with 33 kg of water at 0∘0^\circC. Find the equilibrium temperature.

Example 13

hard
0.40.4 kg of ice at −10∘-10^\circC is added to 11 kg of water at 40∘40^\circC. (cice=2100c_{\text{ice}} = 2100, Lf=334000L_f = 334000, cw=4200c_w = 4200.) Find the equilibrium temperature.

Example 14

medium
Why does a large lake change temperature more slowly than a small puddle under the same sunlight?

Example 15

medium
A large lake at 15∘15^\circC and a teaspoon of water at 15∘15^\circC are in thermal equilibrium. Which has more internal (thermal) energy?

Example 16

medium
A 0.50.5 kg block at 80∘80^\circC is placed in 0.50.5 kg water (c=4200c = 4200) at 20∘20^\circC and they settle at 25∘25^\circC. Find the block's specific heat.

Example 17

medium
2 kg2 \text{ kg} of water at 80∘C80^\circ\text{C} mixes with 3 kg3 \text{ kg} at 30∘C30^\circ\text{C}. Find the equilibrium temperature.

Example 18

hard
Equal masses of two metals X (cX=600c_X = 600) at 100∘100^\circC and Y (cY=200c_Y = 200) at 20∘20^\circC are placed in contact (no other losses). Find the equilibrium temperature.

Example 19

easy
Three objects, each in thermal equilibrium with a fourth, are mixed together. Their temperatures are _____.

Example 20

medium
Heat flows between two objects until equilibrium. Object A loses 800800 J. Object B's temperature rises by 4∘4^\circC with c=1000c = 1000 J/kg·∘^\circC. Find object B's mass.
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