A rubber band is under tension in equilibrium, modeled by the equation t 1 = AT (12 - 1/1) \x2 With t as the tension, T is the absolute temperature, x length of the band, lo is the legth of the band without tension, and A is constant. The thermal capacity at x=lo is cx(x=lo,T) = K, with K as constant. (a) Solve the following as a function of x and T (JE) (i) (ii) (bcx)T (iii) cx(x,T) (iv) E(x,T) and (v) S(x,T) Where E is the energy and S is entropy (b) If the band is stretched adiabatically from x=lo to x=1.510, what is its final temperature?
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- One process for decaffeinating coffee uses carbon dioxide ( M=44.0 g/mol) at a molar density of about 14,0 mol/m3 and a temperature of about 60 . (a) Is CO2 a solid, liquid, gas, or supercritical fluid under those conditions? (b) The van der Waals constants for carbon dioxide are a=0.3658 Pa m6/mol2 and b=4.286105 m3/mol. Using the van der Waals equation, estimate pressure of CO2 at that temperature and density. `Using a numerical integration method such as Simpson's rule, find the fraction of molecules in a sample of oxygen gas at a temperature of 250 K that have speeds between 100 m/s and 150 m/s. The molar mass of oxygen (O2) is 32.0 g/mol. A precision to two significant digits is enough.1. The figure shows the natural loga- rithm of the particle density of air (p = 1.225 kg m-3 at h = 0) for a constant temperature. Given that the linear fit to the data is In(n) = 58.533 at h = 0 and In(n) 57.386 at h = 10ª m, stating any assumptions used, 10 2000 4000 6000 8000 Height, h [m] (a) calculate the average mass of an air particle, (b) determine the temperature of the air. Number density, In(n) [m] 57.5 58 58.5
- The molar heat capacity at constant pressure of carbon dioxide is 29.14 J/K.mol. (a) What is the value of its molar heat capacity at constant volume? J/mol. 4 sig. (b) Calculate the change in enthalpy when 1 mole carbon dioxide is heated from 15°C (the temperature when the air is inhaled) to 37°C (blood temperature, the temperature in our lungs)? number normal format. (c) Calculate molar internal energy when carbon dioxide is heated from 19.16 °C (the temperature when the air is inhaled) to 37°C (blood temperature, the temperature in our lungs). normal format. J/mol 3 sig. number Click Save and Submit to save and submit. Click Save All Answers to save all answers. E R O El 5 G E O A J/K.mol. 4 sig. number H FO 1₂ Save All A 87°F ^!Either give an exact answer, or make sure you include at least 4 significant digits on your answer. The pressure P (in kilopascals), volume V (in liters), and temperature T (in kelvins) of a mole of an ideal gas are related by the equation PV = 8.31T. Find the rate at which the volume is changing when the temperature is 330 K and increasing at a rate of 0.15 K/s and the pressure is 26 and increasing at a rate of 0.03 kPa/s. 1110 L/SWhen the coefficient of linear expansion, a, and the temperature change, T-T, are large, a length L, of a solid substance expands in length to a(T, -T₂) L₁ = L₁e O L=L[1 + a(Tƒ– T;)]. ○ Ly=al (Ty-T). O L=L[1 + In(a(T₁-T))]. a(T, I₂ = ₁₂₁[ 1 + ª²(²₁-7)].
- The vapor pressure is the pressure of the vaporphase of a substance when it is in equilibrium with the solid or liquid phaseof the substance. The relative humidity is the partial pressure of watervapor in the air divided by the vapor pressure of water at that same temperature,expressed as a percentage. The air is saturated when the humidityis 100%. (a) The vapor pressure of water at 20.0C is 2.34 * 10^3 Pa.If the air temperature is 20.0C and the relative humidity is 60%, what isthe partial pressure of water vapor in the atmosphere (that is, the pressuredue to water vapor alone)? (b) Under the conditions of part (a), what is themass of water in 1.00 m3 of air? (The molar mass of water is 18.0 g>mol.Assume that water vapor can be treated as an ideal gas.)Consider a thermocouple that generates the following output for the input temperature T (°C). Find the sensitivity of N(T) (non-linearity function) in unit of pV at T = 10 °C. Write your answer with no decimal point. E(T) = T+ 2T2+3T3 (HV) Tmin=0 and Tmax%3D20 °C.Given a cylindrical Cu bar (length L = 4 m, radius, r = 2 cm). One end is kept in a heat bath at 105 °C and the other temperature at 5 °C. The surface of the bar is insulated so that there is negligible heat loss through it. thermal conductivity of copper: kcu = 385 W/m K Calculate the following up to three (3) significant figures: (1) Thermal resistance Rth of the Cu bar, Ans = (2) Conduction heat current HC, Ans = (3) Temperature gradient AT/Ax, Ans = (4) Temperature T of the Cu bar 0.5 m from the hot end, Ans in W in C/m in K/W in C
- The goal in this problem is to find the growth of an ice layer as a function of time. Call the thickness of the ice layer L. (a) Derive an equation for dL/dt in terms of L , the temperature T above the ice, and the propertiesof ice (which you can leave in symbolic form instead of substituting the numbers). (b) Solve this differential equation assuming that at t = 0 , you have L = 0. If you have studied differential equations, you will know atechnique for solving equations of this type: manipulate the equation to get dL/dt multiplied by a (very simple) function of L on one side, and integrate both sides with respect to time. Alternatively, you may be able to use your knowledge of the derivatives of various functions to guess the solution, which has a simple dependence on t. (c) Will the water eventually freeze to the bottom of the flask?40000cm, and at 1000C its length is 40060cm. (a) What is the linear expansion coefficient of the alloy? (b) what is the temperature when its length is 39975cm? (10) A hole with diameter of 2cm is drilled through a stainless steel pate at room temperature (20OC). By what fraction (Dr/r) will the hole be larger when the plate is heated to 1500C? (11) Calculate the fractional change in volume (Dv/v) of an aluminum bar that undergoes a change in temperature of 300C.Viscosity of fluid plays a significant role in the analyses of many fluid dynamics problems. The viscosity of water can be determined from the following correlation: q10(72,) where e = viscosity (N/s•m²) T- temperature (K) - 2.414 x 10-s 2 - 247.8 (K) s = 14 0 (K) What is the appropriate unit for q, if the above equa- tion is to be homnogeneous in units?