Ten kilograms of steam at 100 ^∘ C is condensed by passing it into 500 kg of water at 40.0^∘ C.

step 1 Good day. The topic is about heat transfer. Heat transfers from a colder body to a colder body.

Ten kilograms of steam at 100 ^∘ C is condensed by passing...

Key Concepts

Conservation of Energy in Thermal Processes

The principle of conservation of energy states that energy cannot be created or destroyed but only transformed from one form to another. In the context of heat transfer, this means that the energy released by the condensing steam and cooling water must be equal to the energy absorbed by the colder water as it warms up, leading to a thermal equilibrium condition where the final temperature can be calculated.

Specific Heat Capacity

Specific heat capacity is the amount of energy required to raise the temperature of one unit mass of a substance by one degree Celsius. It plays a vital role in the problem as it determines how much energy is needed to change the temperature of the water and condensed steam, and it is used to relate the heat transfer during the warming or cooling processes.

Latent Heat of Vaporization/Condensation

This concept refers to the amount of energy released or absorbed when a substance undergoes a phase change between liquid and gas without a temperature change. In the context of the problem, the energy released when steam condenses to water is used to warm the colder water, and understanding this energy transfer is crucial for calculating the final equilibrium temperature.

Transcript

00:01 Good day.

00:02 The topic is about heat transfer.

00:04 Heat transfers from a colder body to a colder body.

00:08 If we neglect heat loss to the surroundings, we say that the heat absorbed by the colder body is equal to the heat that is released by the hotter one.

00:17 In another way of putting it, the sum of the heat that is transferred to or from a system is equal to zero.

00:24 We note that when heat is absorbed or released, it may change the temperature of the substance, and we quantify that that heat that causes temperature change as q equals m, c, delta t, where q is the heat, m is the mass, c is the specific heat, which value can be determined if we know what substance there is, and delta t is the change in temperature which can be solved as the difference between the final temperature tf and the initial temperature t.

00:53 Or when the heat that is absorbed or released by the substance causes the substance to change its face, then we solve that heat as q equals ml, where l is the latent heat.

01:04 And it depends on the type of phase change at the course.

01:08 So, for example, if the substance undergoes vaporization, then the latent heat is in the form of latent heat of vaporization.

01:16 Now let us consider a steam, which mass is 10 kilogram, and at its boiling temperature, which is, 100 degrees celsius is allowed to condense by passing it over into the into 500 kilograms of water at 40 degrees celsius we wish to find the final temperature of the mixing process so we assume that the that after the steam condenses its temperature lowers to a certain tf and that tf is also the same temperature that is attained by the water 500 kilograms of water so we have the queue of the steam, assuming that no heat is lost to the surrounding, plus the queue of water is equal to zero.

02:05 The queue of the steam is composed of the heat that is lost when it condenses plus the heat that it further loses when its temperature drops to tf.

02:17 So we write the heat that is associated when it condenses as m times l, c, whereas, is the heat of condensation plus the heat that is associated when its temperature further drops to tf.

02:34 So we have m -c -t -f minus t -i.

02:41 So since this is steam, so we have steam, this is steam, and note that when steam condenses, it becomes water.

02:49 So we can use the specific heat for water here.

02:53 So next for water we have suppose water in the process changes its temperature only...

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