question stringlengths 326 9.6k | answer stringlengths 1 406 | taskname stringclasses 36
values | doc_id int64 0 670 | o3-mini-high_correct bool 2
classes | o4-mini-high_correct bool 2
classes |
|---|---|---|---|---|---|
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{\frac{\sinh [(2 s+1) x]}{\sinh x}} | ugphysics_StatisticalMechanics | 84 | true | true |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{k + \frac{15 g^{2}}{8 c^{3}} k^{2} T} | ugphysics_StatisticalMechanics | 103 | true | true |
The following is an open-ended problem from Statistical Mechanics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{\frac{p_0}{2} \left( 1 + \mathrm{e}^{-\frac{A \bar{v} t}{2V}} \right)} | ugphysics_StatisticalMechanics | 172 | true | true |
The following is an open-ended problem from Theoretical Mechanics of the undergraduate-level Physics. The answer of The problem should be a range inteval. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in... | \boxed{\left(\frac{b}{2 m}\right)^{2} < (2-\sqrt{2}) \frac{g}{l}} | ugphysics_TheoreticalMechanics | 21 | true | true |
The following is an open-ended problem from Theoretical Mechanics of the undergraduate-level Physics. The problem has multiple answers, each of them should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represe... | \boxed{0.0607, 0.0694} | ugphysics_TheoreticalMechanics | 36 | true | true |
The following is an open-ended problem from Theoretical Mechanics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the... | \boxed{x_{1} = \frac{p}{2 m \omega_{1}} \sin \omega_{1} t + \frac{p M}{2 m (M+2 m) \omega_{2}} \sin \omega_{2} t + \frac{p t}{M+2 m}} | ugphysics_TheoreticalMechanics | 71 | true | true |
The following is an open-ended problem from Thermodynamics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solu... | \boxed{\nu^{\prime}=\frac{\frac{p_{0} V_{0}}{R T_{0}}-\nu_{0}}{\gamma}} | ugphysics_Thermodynamics | 44 | true | true |
The following is an open-ended problem from Thermodynamics of the undergraduate-level Physics. The answer of The problem should be an equation. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the soluti... | \boxed{m = \frac{4 \pi}{3} \frac{M}{R T} r^{3}\left(p_{0} + \frac{4 \sigma}{r}\right)} | ugphysics_Thermodynamics | 123 | true | true |
The following is an open-ended problem from Thermodynamics of the undergraduate-level Physics. The answer of The problem should be either True or False. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in t... | \boxed{No} | ugphysics_Thermodynamics | 136 | true | true |
The following is an open-ended problem from Thermodynamics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and form... | \boxed{m_{1} c T_{0} \ln \frac{T_{1}}{T_{0}}, m_{1} c\left(T_{1}-T_{0}\right)-m_{1} c T_{0} \ln \frac{T_{1}}{T_{0}}} | ugphysics_Thermodynamics | 150 | true | true |
The following is an open-ended problem from Thermodynamics of the undergraduate-level Physics. The problem has multiple answers, each of them should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and form... | \boxed{m_{2} c T_{0} \ln \frac{T_{0}}{T_{2}}, m_{2} c T_{0} \ln \frac{T_{0}}{T_{2}}-m_{2} c\left(T_{0}-T_{2}\right)} | ugphysics_Thermodynamics | 186 | true | true |
The following is an open-ended problem from Wave Optics of the undergraduate-level Physics. The answer of The problem should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas u... | \boxed{7.5} | ugphysics_WaveOptics | 0 | true | true |
The following is an open-ended problem from Wave Optics of the undergraduate-level Physics. The problem has multiple answers, each of them should be a numerical value without units. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the var... | \boxed{17.9, 34.7, 61.9} | ugphysics_WaveOptics | 52 | true | true |
The following is an open-ended problem from Wave Optics of the undergraduate-level Physics. The answer of The problem should be an expression. Please calculate the answer according to the given requirements and the information provided. Please use LaTeX format to represent the variables and formulas used in the solutio... | \boxed{\Delta = \frac{(r + L_0) \lambda}{2r\varphi}} | ugphysics_WaveOptics | 120 | true | true |
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