The temperature of the cooling water as it leaves the hot engine of an automobile is 240 °F. After it passes through the radiator it has a temperature of 175 °F. Calculate the amount of heat transferred from the engine to the surroundings by one gallon of water with a specific heat of 4.184 J/g °C. Type your answer. Next Previous

Chemistry
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**Heat Transfer Calculation in Automobile Radiators**

**Problem Overview:**

The temperature of the cooling water as it leaves the hot engine of an automobile is 240 °F. After it passes through the radiator, the temperature drops to 175 °F. We need to calculate the amount of heat transferred from the engine to the surroundings by one gallon of water. The specific heat capacity of water is 4.184 J/g°C.

**Steps to Solve the Problem:**

1. **Convert Temperatures to Celsius:**
   - Use the conversion formula: \( °C = (°F - 32) \times \frac{5}{9} \).
   - Convert 240 °F and 175 °F to Celsius.

2. **Calculate the Change in Temperature (ΔT):**
   - Find the difference between the initial and final temperatures in Celsius.

3. **Determine the Mass of Water:**
   - Find the mass of one gallon of water in grams.

4. **Calculate Heat Transferred (q):**
   - Use the formula: \( q = m \times c \times ΔT \),
   where \( m \) is the mass of the water, \( c \) is the specific heat capacity, and \( ΔT \) is the temperature change.

**Note:** Ensure all units are consistent, particularly when converting temperatures and calculating heat in Joules, to obtain accurate results.
Transcribed Image Text:**Heat Transfer Calculation in Automobile Radiators** **Problem Overview:** The temperature of the cooling water as it leaves the hot engine of an automobile is 240 °F. After it passes through the radiator, the temperature drops to 175 °F. We need to calculate the amount of heat transferred from the engine to the surroundings by one gallon of water. The specific heat capacity of water is 4.184 J/g°C. **Steps to Solve the Problem:** 1. **Convert Temperatures to Celsius:** - Use the conversion formula: \( °C = (°F - 32) \times \frac{5}{9} \). - Convert 240 °F and 175 °F to Celsius. 2. **Calculate the Change in Temperature (ΔT):** - Find the difference between the initial and final temperatures in Celsius. 3. **Determine the Mass of Water:** - Find the mass of one gallon of water in grams. 4. **Calculate Heat Transferred (q):** - Use the formula: \( q = m \times c \times ΔT \), where \( m \) is the mass of the water, \( c \) is the specific heat capacity, and \( ΔT \) is the temperature change. **Note:** Ensure all units are consistent, particularly when converting temperatures and calculating heat in Joules, to obtain accurate results.
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