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Answer :
Final answer:
The change in internal energy of a system can be calculated using the First Law of Thermodynamics. For the first question, the change in internal energy is 79000 J. For the second question, it requires 28125 J of heat to warm the sand.
Explanation:
The change in internal energy of a system can be calculated using the First Law of Thermodynamics, which states that the change in internal energy is equal to the sum of heat transferred to the system and the work done on the system.
To find the change in internal energy of the system, we use the first law of thermodynamics, which states that the change in internal energy (ΔU) of a system is equal to the heat (Q) added to the system minus the work (W) done by the system. That is, ΔU = Q - W. In this scenario, the system absorbs 196 kJ of heat and the surroundings do 117 kJ of work on the system. The work done 'on' the system contributes to an increase in internal energy, and therefore should be added:
ΔU = Q + W
ΔU = 196 kJ + 117 kJ
ΔU = 313 kJ
Hence, the change in internal energy of the system is 313 kJ.
For the first question, the system absorbs 196 KJ of heat and the surroundings do 117 KJ of work on the system. The change in internal energy can be calculated as follows:
Convert the units of heat and work to joules: 196 KJ = 196,000 J and 117 KJ = 117,000 J.
Subtract the work done from the heat absorbed: Change in internal energy = Heat absorbed - Work done = 196,000 J - 117,000 J = 79,000 J.
For the second question, the amount of heat required to warm the sand can be calculated using the formula:
Heat = Mass x Specific Heat Capacity x Temperature Change
Convert the mass from kg to g: 1.50 kg = 1500 g.
Calculate the temperature change: ΔT = Final Temperature - Initial Temperature = 100.0°C - 25.0°C = 75.0°C.
Use the specific heat capacity of sand (0.25 J/g°C) to calculate the heat: Heat = 1500 g x 0.25 J/g°C x 75.0°C = 28,125 J.
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Final answer:
The change in internal energy of the system is a 313 kJ increase, calculated using the first law of thermodynamics by adding the heat absorbed (196 kJ) to the work done on the system (117 kJ).
Explanation:
The change in internal energy of the system can be calculated using the first law of thermodynamics, which states that the change in internal energy (ΔU) is equal to the heat (ΔQ) added to the system plus the work (ΔW) done on the system. Mathematically, it is expressed as ΔU = ΔQ + ΔW. In the given problem, the system absorbs 196 kJ of heat and the surroundings do 117 kJ of work on the system. Therefore, the change in internal energy (ΔU) is:
ΔU = ΔQ + ΔW
ΔU = 196 kJ + 117 kJ
ΔU = 313 kJ
The system has experienced an increase in internal energy by 313 kJ.
