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3 years ago

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A large room in a house holds 947 kg of dry air at 33.2°C. A woman opens a window briefly and a cool breeze brings in an additio

nal 62.4 kg of dry air at 13.2°C. At what temperature (in degrees Celsius) will the two air masses come into thermal equilibrium, assuming they form a closed system? (The specific heat of dry air is 1006 J/ kg * °C, although that value will cancel out of the calorimetry equation.)
°C

1 answer:

BartSMP [9]3 years ago

7 0

Answer:

31.96362 °C

Explanation:

$m_1$ = Mass of air in the room = 947 kg

$m_2$ = Mass of air entering the room = 62.4 kg

$T_1$ = Temperature in the room = 33.2°C

$T_2$ = Temperature air entering the room = 13.2°C

T = Equilibrium temperature

c = Specific heat of air = 1006 J/kg °C

In the case of thermal equilibrium we have the relation

$m_1c(T_1-T)=m_2c(T-T_2)\\\Rightarrow T=\frac{m_2T_2+m_1T_1}{m_1+m_2}\\\Rightarrow T=\frac{62.4(13.2+273.15)+947(33.2+273.15)}{947+62.4}\\\Rightarrow T=305.11362\ K=305.11362-273.15=31.96362^{\circ}C$

The temperature of thermal equilibrium is 31.96362 °C

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a) Given the existence of non-conservative forces (friction between toboggan and ground), the motion must be modelled by means of the Principle of Energy Conservation and the Work-Energy Theorem, since toboggan decrease its speed (associated with due to the action of friction. Changes in gravitational potential energy can be neglected due to the inclination of the ground. Then:

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$f = \frac{(375\,kg)\cdot \left[\left(4.50\,\frac{m}{s} \right)^{2}-\left(1.20\,\frac{m}{s}\right)^{2}\right]}{2\cdot (5.40\,m)}$

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$\% K_{loss} = \left(1-\frac{K_{2}}{K_{1}} \right)\times 100\,\%$

$\% K_{loss} = \left(1-\frac{\frac{1}{2}\cdot m \cdot v_{2}^{2}}{\frac{1}{2}\cdot m \cdot v_{1}^{2}} \right)\times 100\,\%$

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