Suppose 0.0100 kg of steam (at 100.00^∘ C ) is added to 0.100 kg of water (initially at 19.0^∘

Suppose 0.0100 kg of steam (at 100.00^∘ C ) is added to...

Suppose $0.0100 \mathrm{~kg}$ of steam (at $100.00^{\circ} \mathrm{C}$ ) is added to $0.100 \mathrm{~kg}$ of water (initially at $19.0^{\circ} \mathrm{C}$ ). The water is inside an aluminum cup of mass $35.0 \mathrm{~g} .$ The cup is inside a perfectly insulated calorimetry container that prevents heat exchange with the outside environment. Find the final temperature of the water after equilibrium is reached.

Key Concepts

Conservation of Energy in Calorimetry

This concept refers to the principle that within an isolated system, the total amount of energy remains constant. In calorimetric problems, this means that the heat lost by one component of the system must equal the heat gained by another, enabling the calculation of temperature changes and phase transitions.

Latent Heat of Phase Change

Latent heat is the energy absorbed or released by a substance during a phase transition at constant temperature. In calorimetry, it is critical for processes like condensation or vaporization, where the transfer of latent heat plays a key role in determining the equilibrium state without a change in temperature.

Specific Heat Capacity

Specific heat capacity is a property that indicates the amount of energy required to raise the temperature of a unit mass of a substance by one degree. It is vital in determining how much energy is needed to change the temperature of different substances within a calorimetry problem.

Thermal Equilibrium

Thermal equilibrium is the state reached when all parts of a system achieve a uniform temperature. In calorimetry, after considering all heat exchanges and phase changes, the final temperature is determined by the balance of energy throughout the system.

Transcript

00:01 We have a steam which is placed which is put into the water and water it is put into the aluminum cup okay the cup is inside a perfectly insulated calorimetry so that heat no heat exchange with the environment is taking place so we have to determine the final temperature of the water after equilibrium has been reached so we can write that the heat lost by the steam minus q s this will be equals to the heat gained by the water and aluminum so qw plus q aluminum so now substituting values so it will be equals to minus of heat lost by the steam it will be minus m as multiplied by latent heat of vaporization plus mass of steam multiplied by specific heat of water final equilibrium temperature t equivalent minus t temperature of steam this will be equals to mass of water specific heat of water and t equilibrium minus temperature of water plus heat of aluminum, it will be equals to mass of aluminum, specific heat of aluminum multiplied by equilibrium temperature minus temperature of aluminum which is also equals to the temperature of water.

01:19 So from here after rearranging and we get equilibrium temperature equation t equilibrium, it will be equals to mass m as multiplied by latent heat of vaporization.

01:30 Equation plus mscw t s plus m .w cw tw plus m .a .l.

01:41 C .a .l.

01:42 T .w.

01:44 D .w.

01:53 This will be the final equation for the equilibrium temperature.

01:57 Now substituting values in this equation, so we get we are substituting mass in the gram and temperature in the kelvin.

02:05 So substituting values, so we get the equilibrium equals to 10 gram multiplied by latent heat of vaporization is 539 for the water plus mass of steam is 10 gram and specific heat of water is 1 in the calorie per gram kelvin and temperature is 100 degree centigrade for the water.

02:27 So it can be converted into kelvin.

02:29 So it will be 373 plus mass of water is 100 gram...

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