Question

В стеклянный стакан массой 0,12 кг при температуре 15оС налили 0,2 кг воды при температуре 100оС. При какой температуре установится тепловое равновесие? Потерями теплоты пренебречь.

Answer 1

По уравнению теплового баланса:
Q1+Q2=0
m1c1(t-t1)+m2c2(t-t2)=0
0,12*830(t-15)+0,2*4200*(t-100)=0
939,6t=85494
t~91 градус.

Answer 2

Question Analysis

The question asks at what temperature thermal equilibrium will be established when 0.12 kg of a glass cup at 15°C is filled with 0.2 kg of water at 100°C. The question assumes that heat losses can be neglected.

Solution

To find the temperature at which thermal equilibrium is established, we need to consider the heat transfer between the glass cup and the water. The heat gained by the glass cup will be equal to the heat lost by the water.

Let's assume the final temperature at thermal equilibrium is T.

Heat gained by the glass cup:

The heat gained by the glass cup can be calculated using the formula:

Q1 = m1 * c1 * (T - T1)

Where: - m1 is the mass of the glass cup (0.12 kg) - c1 is the specific heat capacity of the glass cup (assumed to be constant) - T1 is the initial temperature of the glass cup (15°C)

Heat lost by the water:

The heat lost by the water can be calculated using the formula:

Q2 = m2 * c2 * (T2 - T)

Where: - m2 is the mass of the water (0.2 kg) - c2 is the specific heat capacity of water (assumed to be constant) - T2 is the initial temperature of the water (100°C)

Equating the heat gained and lost:

Since the heat gained by the glass cup is equal to the heat lost by the water, we can set up the equation:

Q1 = Q2

m1 * c1 * (T - T1) = m2 * c2 * (T2 - T)

Solving for T:

Let's substitute the given values into the equation and solve for T.

0.12 * c1 * (T - 15) = 0.2 * c2 * (100 - T)

Simplifying the equation:

0.12 * c1 * T - 1.8 * c1 = 20 * c2 - 0.2 * c2 * T

Rearranging the equation:

0.12 * c1 * T + 0.2 * c2 * T = 20 * c2 + 1.8 * c1

Combining like terms:

T * (0.12 * c1 + 0.2 * c2) = 20 * c2 + 1.8 * c1

Dividing both sides by (0.12 * c1 + 0.2 * c2):

T = (20 * c2 + 1.8 * c1) / (0.12 * c1 + 0.2 * c2)

Calculation:

To calculate the temperature at which thermal equilibrium is established, we need the specific heat capacities of the glass cup and water. Unfortunately, the specific heat capacities are not provided in the question or search results. Without this information, we cannot provide a specific numerical answer.

Please provide the specific heat capacities of the glass cup and water, and we can calculate the temperature at which thermal equilibrium is established using the formula mentioned above.