The specific heat capacity of a substance is the quantity of heat power required to raise the temperature the 1 kg of the substance by 1°C. The symbol offered for specific heat capacity is c and also the units are J/(kg °C) or J/(kg K). (Note that these devices may additionally be composed as J kg–1 °C–1 or J kg–1 K–1).

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Some usual values of certain heat capacity for the variety of temperature 0°C to 100°C include:

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Hence to raise the temperature the 1 kg of steel by 1°C calls for 500 J of energy, come raise the temperature the 5 kg of iron by 1°C needs (500 × 5) J of energy, and to raise the temperature that 5 kg of steel by 40°C again- quires (500 × 5 × 40) J of energy, i.e. 100 kJ.

In general, the quantity of warm energy, Q, required to raise a fixed m kg of a substance through a specific heat volume of c J/(kg °C), indigenous temperature t1 °C come t2 °C is provided by:

Q = mc(t2 – t1) joules

Problem 3. Calculate the amount of heat forced to advanced the temperature of 5 kg of water indigenous 0°C come 100°C. Assume the details heat capacity of water is 4200 J/(kg °C).

Quantity of heat energy,

Q = mc(t2 – t1)

= 5 kg × 4200 J/(kg °C) × (100 – 0)°C

= 5 × 4200 × 100

= 2100000 J or 2100 kJ or 2.1 MJ

Problem 4. A block of cast iron having actually a fixed of  10 kg cools native a temperature the 150°C to 50°C.

How much power is lost by the actors iron? i think the specific heat volume of iron is 500 J/(kg °C).

Quantity of warm energy,

Q = mc(t2 – t1)

= 10 kg × 500 J/(kg °C) × (50 – 150)°C

= 10 × 500 × (–100)

= – 500000 J or – 500 kJ or – 0.5 MJ

(Note that the minus sign suggests that warmth is given out or lost).

Problem 5. Some lead having a specific heat volume of 130 J/(kg °C) is heated from 27°C come its melting point at 327°C. If the quantity of heat forced is 780 kJ, recognize the mass of the lead.

Quantity the heat, Q = mc(t2 – t1), hence,

780 × 103 J = m × 130 J/(kg °C) × (327 – 27)°C i.e. 780000 = m × 130 × 300

from which, mass, m = 780000/130*300 kg = 20 kg

Problem 6. 273 kJ the heat power are compelled to progressive the temperature that 10 kg the copper indigenous 15°C to 85°C. Identify the particular heat capacity of copper.

Quantity that heat, Q = mc(t2 – t1), hence: 273 × 103 J = 10 kg × c × (85 – 15)°C where c is the specific heat capacity, i.e. 273000 = 10 × c × 70 from which, particular heat capacity, c = 273000/10 × 70 = 390 J/(kg °C

Problem 7. 5.7 MJ the heat energy are gave to 30 kg that aluminium the is at first at a temperature the 20°C. If the details heat volume of aluminium is 950 J(kg°C), identify its final temperature.

of 20°C. If the certain heat volume of aluminium is 950 J(kg°C), determine its final temperature.

Quantity of heat,

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Problem 8. A copper container of fixed 500 g includes 1 litre the water in ~ 293 K. Calculate the amount of heat required to progressive the temperature the the water and container to boiling point, assuming there space no warm losses. Assume that the certain heat volume of copper is 390 J/(kg K), the particular heat capacity of water is 4.2 kJ(kg K) and also 1 litre that water has a mass of 1 kg.

Heat is forced to raise the temperature that the water, and also to progressive the temperature the the copper container.

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Practise exercise 107 Further problems on details heat capacity

1. Determine the amount of heat power (in megajoules) required to progressive the tem- perature of 10 kg that water native 0°C to 50°C. I think the specific heat capacity of water is 4200 J/(kg °C). <2.1 MJ>

2. Some copper, having actually a massive of 20 kg, cools native a temperature that 120°C to 70°C. If the certain heat volume of copper is 390 J/(kg °C), exactly how much heat energy is shed by the copper ? <390 kJ>

3. A block that aluminium having actually a certain heat volume of 950 J/(kg °C) is heated from 60°C to its melting suggest at 660°C. If the quantity of heat forced is 2.85 MJ, de- termine the massive of the aluminium block. <5 kg>

4. 20.8 kJ of heat power is forced to advanced the temperature that 2 kg of command from 16°C come 96°C. Determine the particular heat capacity of lead. <130 J/kg °C>

5. 250 kJ of heat energy is gave to 10 kg of stole which is at first at a temperature of 15°C. If the certain heat volume of iron is 500 J/(kg °C) recognize its last tempera- ture. <65°C>

Change that state

A product may exist in any kind of one that three states – solid, liquid or gas. If warmth is provided at a continuous rate to some ice initially at, say, –30°C, its temperature rises as shown in number 20.1. At first the temperature in- creases native –30°C to 0°C as shown by the heat AB. It climate remains consistent at 0°C for the moment BC required for the ice to melt right into water.

When melting commences the power gained by regular heating is balance out by the energy required because that the adjust of state and also the temperature remains continuous even though heating is continued. As soon as the ice is completely melted to water, regular heating raises the temperature to 100°C, as presented by CD in figure 20.1. The water then begins to boil and also the temperature

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again remains consistent at 100°C, presented as DE, until all the water has vaporised.

Continual heater raises the temperature of the heavy steam as presented by EF in the region where the heavy steam is termed superheated.

Changes that state indigenous solid to fluid or liquid to gas happen without change of temperature and also such alters are reversible processes. Once heat power flows come or from a substance and also causes a adjust of temperature, such as between A and also B, in between C and also D and be- tween E and F in figure 20.1, it is called sensible heat (since it can be ‘sensed’ by a thermometer).

Heat power which operation to or from a substance while the temperature stays constant, such together be- tween B and C and between D and also E in number 20.1, is referred to as latent warm (latent method concealed or hidden).

Problem 9. Steam originally at a temperature of 130°C is cooled come a temperature the 20°C below the freezing suggest of water, the lose of heat energy being in ~ a consistent rate. Do a sketch, and also briefly explain, the meant temperature/time graph rep- resenting this change.

A temperature/time graph representing the readjust is shown in figure 20.2. Initially steam cools till it reaches the boiling point of water at 100°C. Tempera- ture then remains constant, i.e. In between A and also B, even though it is still giving off warm (i.e. Implicitly heat). Once all the steam at 100°C has changed to water in ~ 100°C that starts come cool again until it get the freezing allude of water in ~ 0°C. Native C to D the temperature again remains consistent (i.e. Implicitly heat), until all the water is converted to ice. The temperature that the ice cream then decreases together shown.

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Practise exercise 108 A further trouble on adjust of state

1. Some ice, initially at – 40°C, has heat sup- plied come it at a consistent rate till it becomes superheated steam at 150°C. Map out a typical temperature/time graph expected and use the to describe the difference in between sensible and latent heat.