dT = k(T- Tm), where T(t) is the temperature of the object at The mathematical model for Newton's law of cooling is dt time t and Tm is the constant temperature of the surrounding medium. What is lim T(t) ?

This is a question from my problem sheet with the answers. i dont understand how to answer this question. Please use this book for the values: Thermodynamic and Transport Properties of Fluids by Rogersand Mayhew.

A graduate student wants to use van der Waals' equation to express the pressure-volume- temperature relations for a gas. Her project requires a reasonable degree of precision in the p-V-T calculations. Therefore, she made the following experimental measurements with her setup to get an idea of how easy the experiment would be: Temperature, K Pressure, atm Volume, ft'/lb mol 273.1 273.1 200 1.860 1000 0.741 Determine values of constants a and b to be used in van der Waals' equation that best fit the experimental data.

A hot small copper ball [c in kJ/kg.°C, k in W/m.°C] is suddenly placed in water maintained at 100 °C. The convection heat transfer coefficient is h in W/m². ºC. Derive equation to calculate the time required to reduce ball to temperature T.

The van der Waals (vdW) equation is a cubic equation of state (CEOS) which may be used to calculate the volume or pressure conditions for a real gas: P= a = RT a v-b v² Here, v represents the molar volume of the gas, and P, R, and T' are the absolute pressure, ideal gas constant, and absolute temperature of the gas, respectively. The values a and b are component dependent an may be calculated using: 27 R²T² 64 P C and b= 1 RT 8 Pc So, when both the critical pressure (Pc) and critical temperature (Tc) are known, one can apply the vdW CEOS to give a more accurate calculate more accurate properties than the ideal gas law. One must be careful to use absolute values for the pressure & temperature (e.g., unit of K not °C) and a value for the gas constant that is consistent with the unit desired (such as R = 0.0083144598 L·bar/K·mol) Do the following: a) Calculate the molar volume (L/mol) of nitrogen gas (Pc = 33.96 bar, Tc = 126.19 K) at 5 bar and 30°C using both the ideal gas law & using…

Unit systema) Determine the units of pressure in the equation pv=RT v: specific volume, m3/kg R: constant in kJ/kgK, T: temperature in K

fet), force force, f 10 Newt. m2 f k, 10sec m, = 10 kg, ma= 20 kg , b= 20 Newton m/sec k, = 30 Newton kz = 60 Newton z, and z are measured with respeet to eguilibrium conditions and all imitial conditions are zero, 1) Write the Newton's second Lau for m, amd m2 2) Derive a statespace represrentation of the conditions : eystem fallowing 2a) only z, is measured 26) only z, is measured 2c) (2,-z,) is measured. un der 3) Derive the following transfor fumetione fG) z,(5) Go G,6) ? G6) ? 4) Describe a mechanical device that can be used to implement the external force fee) as shoun'a bove. 5) Using (Csim) function of MATLAB, plot z,(t), 2, (t)- =, (+)] Zz (t) and

*3.2 PQ1 A 100 mm diameter sphere contains an ideal gas at 20°C. Apply the grid method (p. 9) to calculate the density in units of kg/m³. a. Gas is helium. Gage pressure is 20 in H,O. b. Gas is methane. Vacuum pressure is 3 psi.

Q3 please thanks

Number 16