Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. Portion A has a mass m and a temperature of 97.0 °C, portion B also has a mass m but a temperature of 80.0 °C, and portion C has a mass mc and a temperature of 40.0 °C. What must be the mass of portion C so that the final temperature Tf of the three-portion mixture is T₁ = 50.0 °C? Express your answer in terms of m; for example, mc = 2.20 m. mc = Number i Units

College Physics
11th Edition
ISBN:9781305952300
Author:Raymond A. Serway, Chris Vuille
Publisher:Raymond A. Serway, Chris Vuille
Chapter1: Units, Trigonometry. And Vectors
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**Problem Description:**

Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. The conditions are as follows:

- **Portion A:** 
  - Mass = \( m \)
  - Temperature = 97.0°C

- **Portion B:** 
  - Mass = \( m \)
  - Temperature = 80.0°C

- **Portion C:** 
  - Mass = \( m_C \)
  - Temperature = 40.0°C

**Objective:**

Determine the mass of portion C (\( m_C \)) such that the final temperature (\( T_f \)) of the three-portion mixture is 50.0°C. Express your answer in terms of \( m \). For example, \( m_C = 2.20 \, m \).

**Equation to use:**

The box to input your calculation for \( m_C \) is available with the unit set to be a multiple of \( m \).
Transcribed Image Text:**Problem Description:** Three portions of the same liquid are mixed in a container that prevents the exchange of heat with the environment. The conditions are as follows: - **Portion A:** - Mass = \( m \) - Temperature = 97.0°C - **Portion B:** - Mass = \( m \) - Temperature = 80.0°C - **Portion C:** - Mass = \( m_C \) - Temperature = 40.0°C **Objective:** Determine the mass of portion C (\( m_C \)) such that the final temperature (\( T_f \)) of the three-portion mixture is 50.0°C. Express your answer in terms of \( m \). For example, \( m_C = 2.20 \, m \). **Equation to use:** The box to input your calculation for \( m_C \) is available with the unit set to be a multiple of \( m \).
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