Exercises on calorimetry

exercises on calorimetry

On this page you will find a collection of exercises on calorimetry.
This is a fundamental branch of thermodynamics that deals with the study of heat variations in physical systems. Through the use of instruments called calorimeters, it is possible to determine the changes in heat energy that accompany changes of state, chemical reactions and other phenomena.

Through these exercises, you will have the opportunity to apply the theoretical concepts you have learned and to develop a deeper understanding of the laws of calorimetry.
Each exercise is accompanied by a detailed solution that explains the method of solving step by step, highlighting the physical laws and mathematical formulas used.

This collection is designed for high school students and physical science enthusiasts who want to deepen their knowledge and improve their problem-solving skills.
Dive into the world of calorimetry and learn how it affects thermodynamic systems. Good luck with your work!

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Exercises on calorimetry

1

On the specific heat

Suppose we supply an amount of heat $Q = 3.4 \cdot 10^3 \J$ to a block of iron mass $m = 2.0 \ kg$ . If the specific heat of iron is $c = 4.6 \cdot 10^2 \ J/(kg \cdot K)$

Calculates the change in temperature $\Delta T$ of the block

[ $3,7 \ K$ ]

2

On heat capacity

Suppose we supply an amount of heat $Q = 3.4 \cdot 10^3 \J$ to a ground copper block $m$ . If the specific heat of copper is $c = 3.9 \cdot 10^2 \ J/(kg \cdot K)$ and the temperature change that the block undergoes is $\Delta T = 8.0 \ K$

Calculate the heat capacity $C$ of the block

[ $3.5 \ J/K$ ]

3

On the latent heat of fusion of ice

Suppose we have an ice cube of mass. $m = 3.5 \ kg$ . If the latent heat of fusion of the ice is $\lambda_f = 3.3 \cdot 10^5 \ J/kg$

Calculate the heat $Q$ needed to melt the cube

[ $1.2 \cdot 10^6 \J$ ]

4

A simple exercise on the calorimeter of mixtures

Suppose we have a thermally insulated vessel containing $m_a = 2.50 \ kg$ of water at the temperature $T_a = 300 \ K$ . A block of an unknown metal mass is then placed inside the vessel. $m_b = 3.00 \ kg$ at the temperature $T_b = 400 \ K$ . If the system reaches an equilibrium temperature of $T_{eq} = 360 \ K$

metal cube in a water-filled cylinder

Calculate the specific heat $c_b$ metal

[Hint: The specific heat of water is. $c_a = 4.19 \cdot 10^3 \ J/(kg \cdot K)$ ]

[ $5.24 \cdot 10^3 \ J/(kg \cdot K)$ ]

5

On irradiance and radiated power.

A spherical bulb of radius $r = 0.55 \ m$ Is capable of radiating heat with a power of $P = 5.35 \cdot 10^2 \ W$ . If the bulb reaches a temperature of $T = 400 \ K$

lamp emitting radiation

Calculates the emittance $\epsilon$ of the bulb

[ $0,12$ ]

6

On conduction and Fourier's law

A square side window $L = 0.5 \ m$ and thickness $d = 0.2 \ m$ Is composed of glass of thermal conductivity $k = 0.8 \ W/(m \cdot K)$ . If after $t = 1 \ min$ The difference between the outdoor temperature and the indoor temperature is $\Delta T = 20 \ K$

a window emitting heat

Calculate the heat $Q$ traded per minute

[ $20 \ J/min$ ]

7

On the heat exchanged and the calculation of temperature

A bulk aluminum container $m_a = 2.1 \ kg$ and specific heat $c_a = 8.8 \cdot 10^2 \ J/(kg \cdot K)$ Is initially found at room temperature $T_a = 300 \ K$ . Inside the container is poured $m_b = 1.0 \ kg$ of specific heat oil $c_b = 2.0 \cdot 10^3 \ J/(kg \cdot K)$ until the vessel and the oil reach an equilibrium temperature $T_{eq} = 320 \ K$

two cylinders, one filled with water and one empty

Calculates the initial temperature of the oil $T_b$

[ $338 \ K$ ]

8

On the equilibrium temperature

A mass $m_1 = 2.5 \ kg$ of oil at the temperature $T_1 = 350 \ K$ is mixed with a mass $m_2 = 4.5 \ kg$ Of the same oil at the temperature $T_2 = 370 \ K$ . If the specific heat of the oil is $c = 2.0 \cdot 10^3 \ J/(kg \cdot K)$

Calculate the equilibrium temperature $T_{eq}$

[ $363 \ K$ ]

9

On the temperature of water vapor

To a mass $m = 1.50 \ kg$ of water at the temperature $T_1 = 300 \ K$ An amount of heat is supplied equal to $Q = 8.00 \cdot 10^6 \ J$

Calculate the final temperature $T_f$ of water vapor

[Hint: The specific heat of water is. $c = 4.19 \cdot 10^3 \ J/(kg \cdot K)$ ; the latent heat of evaporation is $\lambda_{ev} = 2.26 \cdot 10^6 \ J/kg$ ; the specific heat of water vapor is. $c_{vap} = 1.90 \cdot 10^3 \ J/(kg \cdot K)$ ]

[ $1.55 \cdot 10^3 \K$ ]

10

On the solidification of water

A mass ice cube $m_1$ and temperature $T_1 = 258 \ K$ is immersed in a vessel containing $m_2 = 1.6 \ kg$ of water at the temperature $T_2 = 273 \ K$ . If at the equilibrium temperature $T_{eq} = 273 \ K$ the mass of ice is equal to $m_3 = 0.8 \ kg$

Calculate the initial mass of ice $m_1$

[Hint: The specific heat of ice is. $c = 2.0 \cdot 10^3 \ J/(kg \cdot K)$ ; the latent heat of solidification of water is $\lambda_s = 3.3 \cdot 10^5 \ J/kg$ ]

[ $0.73 \ kg$ ]

11

On the latent heat of fusion of a metal

A bulk copper block $m = 2.5 \ kg$ and latent heat of fusion equal to $\lambda_f = 21 \cdot 10^4 \ J/kg$ is initially found at the temperature $T_1 = 350 \ K$ . The block is then heated providing an amount of heat equal to $Q = 0.8 \cdot 10^6 \J$ . If the melting temperature of copper is $T_f = 1085 \ K$

Can we say that the whole copper block melts?

[Hint: The specific heat of copper is. $c = 3.9 \cdot 10^2 \ J((kg \cdot K))$ ]

[we cannot]

12

On a glass vessel

A bulk copper block $m_1 = 1.5 \ kg$ at the temperature $T_1 = 500 \ K$ is immersed in a glass vessel of mass $m_2 = 2.8 \ kg$ which contains a mass of water equal to $m_3 = 2.2 \ kg$ at room temperature $T_2 = 300 \ K$ . Assuming that the system does not exchange heat with the external environment.

Calculate the equilibrium temperature $T_{eq}$

[Hint: The specific heat of copper is. $c_1 = 3.9 \cdot 10^2 \ J/(kg \cdot K)$ ; the specific heat of glass is $c_2 = 6.3 \cdot 10^2 \ J/(kg \cdot K)$ ; the specific heat of water is $c_3 = 4.2 \cdot 10^3 \ J/(kg \cdot K)$ ]

[ $309 \ K$ ]

13

On the conservation of energy and heat

A mass copper bullet $m_1 = 0.8 \ kg$ is fired with velocity $v_1 = 1.8 \cdot 10^2 \m/s$ Toward a stationary target of aluminum mass $m_2 = 1.2 \ kg$ . The projectile and target are initially at room temperature $T_1 = T_2 = T = 300 \ K$ . If the impact is completely inelastic and no heat exchange occurs with the external environment

a bullet impacting a metal wall

Calculate the equilibrium temperature $T_{eq}$ Of the projectile + target system

[Hint: The specific heat of copper is. $c_1 = 3.9 \cdot 10^2 \ J/(kg \cdot K)$ ; the specific heat of aluminum is $c_2 = 9.0 \cdot 10^2 \ J/(kg \cdot K)$ ]

[ $306 \ K$ ]

14

On the calorimeter of mixtures and three masses of oil at different temperatures

Consider three masses of oil $m_1 = 1.0 \ kg$ at temperature $T_1 = 320 \ K$ , $m_2 = 1.3 \ kg$ at temperature $T_2 = 346 \ K$ and $m_3 = 1.8 \ kg$ at temperature $T_2 = 305 \ K$ . If these are mixed within a calorimeter of the mixtures.

Calculate the equilibrium temperature $T_{eq}$

[Hint: The specific heat of oil is. $c = 2.0 \cdot 10^3 \ J/(kg \cdot K)$ ]

[ $322 \ K$ ]

15

On the calculation of specific heat

A block of unknown bulk material $m_1 = 1.5 \ kg$ at the temperature $T_1 = 600 \ K$ Is immersed in a vessel of thermal capacity $C = 250 \ J/kg$ which contains a mass of water equal to $m_2 = 2.2 \ kg$ at room temperature $T_2 = 300 \ K$ . Assuming that the system does not exchange heat with the external environment, the system reaches an equilibrium temperature of $T_{eq} = 380 \ K$

Calculate the specific heat of the unknown material

[Hint: The specific heat of water is. $c = 4.2 \cdot 10^3 \ J/(kg \cdot K)$ ]

[ $2.2 \cdot 10^3 \ J/(kg \cdot K)$ ]

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