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title: "A student conducts an experiment to determine the specific heat capacity \\(c_s\\) of an unknown solid sample of mass \\(m_s\\). The sample is heated to an initial temperature \\(T_s\\) and placed into a calorimeter container of mass \\(m_c\\) and specific heat capacity \\(c_c\\). The container holds a mass \\(m_w\\) of water with specific heat capacity \\(c_w\\), initially at temperature \\(T_i\\) (where \\(T_s > T_i\\)). The system reaches a final equilibrium temperature \\(T_f\\) after a time interval \\(\\Delta t\\), during which heat is lost to the surroundings at a constant rate \\(P_{\\text{loss}}\\). Which of the following is a correct expression for \\(c_s\\)?"
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url: "https://nerd-notes.com/ubq/116268/"
date_modified: "2026-08-03T11:46:34+00:00"
---

# A student conducts an experiment to determine the specific heat capacity \(c_s\) of an unknown solid sample of mass \(m_s\). The sample is heated to an initial temperature \(T_s\) and placed into a calorimeter container of mass \(m_c\) and specific heat capacity \(c_c\). The container holds a mass \(m_w\) of water with specific heat capacity \(c_w\), initially at temperature \(T_i\) (where \(T_s > T_i\)). The system reaches a final equilibrium temperature \(T_f\) after a time interval \(\Delta t\), during which heat is lost to the surroundings at a constant rate \(P_{\text{loss}}\). Which of the following is a correct expression for \(c_s\)?

A student conducts an experiment to determine the specific heat capacity \(c_s\) of an unknown solid sample of mass \(m_s\). The sample is heated to an initial temperature \(T_s\) and placed into a calorimeter container of mass \(m_c\) and specific heat capacity \(c_c\). The container holds a mass \(m_w\) of water with specific heat capacity \(c_w\), initially at temperature \(T_i\) (where \(T_s > T_i\)). The system reaches a final equilibrium temperature \(T_f\) after a time interval \(\Delta t\), during which heat is lost to the surroundings at a constant rate \(P_{\text{loss}}\). Which of the following is a correct expression for \(c_s\)?

![A cutaway schematic of an insulated calorimeter cup of mass \(m_c\) containing water of mass \(m_w\) at initial temperature \(T_i\). A solid metal sample block of mass \(m_s\) at initial temperature \(T_s\) is submerged inside the water. Red dashed arrows point from the water toward the outer wall of the calorimeter, labeled \(P_{\text{loss}}\), indicating heat transfer to the environment. Labels identify \(m_s\), \(m_w\), and \(m_c\). No other labels, lines, text, or axes appear.](https://nerd-notes.com/wp-content/uploads/ubq-frq-generated/calorimeter-setup-1785757593-x4HuAS.jpg)

- **A.** \(\dfrac{(m_w c_w + m_c c_c)(T_f - T_i) + P_{\text{loss}} \Delta t}{m_s (T_s - T_f)}\)
- **B.** \(\dfrac{(m_w c_w + m_c c_c)(T_f - T_i) - P_{\text{loss}} \Delta t}{m_s (T_s - T_f)}\)
- **C.** \(\dfrac{m_w c_w (T_f - T_i) + P_{\text{loss}} \Delta t}{m_s (T_s - T_f)}\)
- **D.** \(\dfrac{(m_w c_w + m_c c_c)(T_f - T_i) + P_{\text{loss}} \Delta t}{m_s (T_f - T_i)}\)

*The answer key and step-by-step explanation are available to logged-in users at https://nerd-notes.com/ubq/116268/*